151
Views
103
CrossRef citations to date
0
Altmetric
Original Articles

Braided bialgebras and quadratic blalgebras

Pages 1731-1749 | Received 01 Nov 1991, Published online: 27 Jun 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (25)

Q.-G. Chen & D.-G. Wang. (2016) A Class of Coquasitriangular Hopf Group Algebras. Communications in Algebra 44:1, pages 310-335.
Read now
Tianshui Ma & Haiying Li. (2015) On Radford Biproduct. Communications in Algebra 43:9, pages 3946-3966.
Read now
Tianshui Ma, Haiying Li & Zhicheng Zhang. (2014) Two Results on Brzeziński π-crossed Product. Communications in Algebra 42:5, pages 2082-2098.
Read now
Alessandro Ardizzoni, Margaret Beattie & Claudia Menini. (2011) Cocycle Deformations for Liftings of Quantum Linear Spaces. Communications in Algebra 39:12, pages 4518-4535.
Read now
Tianshui Ma & Shuanhong Wang. (2010) A Method to Construct Oriented Quantum Algebras. Communications in Algebra 38:11, pages 4234-4254.
Read now
Xiao-Li Fang & Li-Hui Zhao. (2010) The Antipode of a Braided Dual Quasi-Hopf Algebra is Bijective. Communications in Algebra 38:7, pages 2448-2453.
Read now
Tianshui Ma & Shuanhong Wang. (2010) General Double Quantum Groups. Communications in Algebra 38:2, pages 645-672.
Read now
Margaret Beattie & Daniel Bulacu. (2009) On the Antipode of a Co-Frobenius (Co)Quasitriangular Hopf Algebra. Communications in Algebra 37:9, pages 2981-2993.
Read now
Hu Guo Quan & Xu Yong Hua. (2008) Twisted Comodule Algebras and the Generalized Quantum Double. Communications in Algebra 36:2, pages 604-621.
Read now
Huixiang Chen & Yinhuo Zhang. (2007) Cocycle Deformations and Brauer Groups. Communications in Algebra 35:2, pages 399-433.
Read now
Andrés Abella & Nicolás Andruskiewitsch. (2002) COMPACT MATRIX QUANTUM GROUPS ARISING FROM HERMITIAN YANG-BAXTER COALGEBRAS. Communications in Algebra 30:7, pages 3107-3142.
Read now
Maozheng Guo, Lining Jiang & Ervin Yunwei Zhao. (2002) THE CONSTRUCTION OF BRAID HOPF ALGEBRA. Communications in Algebra 30:4, pages 1725-1750.
Read now
Giovanna Carnovale. (2001) SOME ISOMORPHISMS FOR THE BRAUER GROUPS OF A HOPF ALGEBRA. Communications in Algebra 29:11, pages 5291-5305.
Read now
Louis Kauffman & David E. Radford. (2000) Quantum algebras, quantum coalgebras, invariants of 1-1 tangles and knots. Communications in Algebra 28:11, pages 5101-5156.
Read now
Zhengming Jiao. (2000) Skew dual bases and the quasitriangular structure of B⋈T H . Communications in Algebra 28:7, pages 3515-3522.
Read now
Shuan-hong Wang. (1999) On braided hopf algebra structures over the twisted smash products . Communications in Algebra 27:11, pages 5561-5573.
Read now
Konard Schmüdgen. (1999) On coquasitriangular bialgebras. Communications in Algebra 27:10, pages 4919-4928.
Read now
Ralf Günther. (1999) Crossed products for pointed hopf algebras. Communications in Algebra 27:9, pages 4389-4410.
Read now
Di-Ming Lu. (1999) Braided yang-baxter operators. Communications in Algebra 27:5, pages 2503-2509.
Read now
Satoshi Suzuki. (1999) Minimal multt-braided bialgebras. Communications in Algebra 27:1, pages 357-386.
Read now
Shuanhong Wang, Zhengming Jiao & Wenzheng Zhao. (1998) Hopf algebra structures on crossed products . Communications in Algebra 26:4, pages 1293-1303.
Read now
Peter Schauenburg. (1996) Hopf bigalois extensions. Communications in Algebra 24:12, pages 3797-3825.
Read now
Yukio Doi & Mitsuhiro Takeuchi. (1995) Quaternion algebras and hopf crossed products. Communications in Algebra 23:9, pages 3291-3325.
Read now
Yukio Doi & Mitsuhiro Takeuch. (1994) Multiplication alteration by two-cocycles - the quantum version. Communications in Algebra 22:14, pages 5715-5732.
Read now

Articles from other publishers (78)

Michael Brannan, Floris Elzinga, Samuel J Harris & Makoto Yamashita. (2023) Crossed Product Equivalence of Quantum Automorphism Groups of Finite Dimensional C*-Algebras. International Mathematics Research Notices 2023:20, pages 17749-17787.
Crossref
José Nicanor ALONSO ÁLVAREZ, J.m. FERNADEZ VILABOA & Ramon GONZALEZ RODRİGUEZ. (2022) Invertible skew pairings and crossed products for weak Hopf algebras. Hacettepe Journal of Mathematics and Statistics 51:6, pages 1600-1620.
Crossref
Daniel Gromada & Moritz Weber. (2022) Generating linear categories of partitions. Kyoto Journal of Mathematics 62:4.
Crossref
Daniel Gromada. (2022) Some examples of quantum graphs. Letters in Mathematical Physics 112:6.
Crossref
Hongdi Huang, Van C. Nguyen, Charlotte Ure, Kent B. Vashaw, Padmini Veerapen & Xingting Wang. (2022) Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation. Transformation Groups.
Crossref
Armando Reyes & Fabio Calderón. (2022) Some interactions between Hopf Galois extensions and noncommutative rings. Universitas Scientiarum 27:2, pages 58-161.
Crossref
J.N. Alonso Álvarez, J.M. Fernández Vilaboa & R. González Rodríguez. (2022) Cocycle deformations for Hom-Hopf algebras. Journal of Algebra 601, pages 354-389.
Crossref
Julien Bichon & Maeva Paradis. (2022) Some isomorphism results for graded twistings of function algebras on finite groups. Annales de la Faculté des sciences de Toulouse : Mathématiques 31:2, pages 501-544.
Crossref
Julien Bichon. (2022) On the monoidal invariance of the cohomological dimension of Hopf algebras. Comptes Rendus. Mathématique 360:G5, pages 561-582.
Crossref
Senlin Zhang & Shuanhong Wang. (2022) A New Approach to Braided T-Categories and Generalized Quantum Yang–Baxter Equations. Mathematics 10:6, pages 968.
Crossref
Serge Skryabin. (2021) Flatness over PI coideal subalgebras. Israel Journal of Mathematics 245:2, pages 735-772.
Crossref
Jyotishman Bhowmick & Sugato Mukhopadhyay. (2021) Pseudo-Riemannian metrics on bicovariant bimodules. Annales Mathématiques Blaise Pascal 27:2, pages 159-180.
Crossref
O. Márquez, D. Bagio, J. M. J. Giraldi & G. A. García. (2020) Finite-dimensional Nichols algebras over dual Radford algebras. Journal of Algebra and Its Applications 20:01, pages 2140001.
Crossref
J. N. Alonso Álvarez, J. M. Fernández Vilaboa & R. González Rodríguez. (2020) Multiplication Alteration by Two-Cocycles: The Non-associative Version. Bulletin of the Malaysian Mathematical Sciences Society 43:5, pages 3557-3615.
Crossref
Pavel Etingof & Shlomo Gelaki. (2020) Invariant Hopf 2-Cocycles for Affine Algebraic Groups. International Mathematics Research Notices 2020:2, pages 344-366.
Crossref
Fernando Fantino, Gastón Andrés García & Mitja Mastnak. (2019) On finite-dimensional copointed Hopf algebras over dihedral groups. Journal of Pure and Applied Algebra 223:8, pages 3611-3634.
Crossref
Mitsuhiro Takeuchi. 2019. Hopf Algebras and Quantum Groups. Hopf Algebras and Quantum Groups 241 260 .
Adriana Mejía Castaño, Susan Montgomery, Sonia Natale, Maria D. Vega & Chelsea Walton. (2018) Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension p3 and pq2. Journal of Pure and Applied Algebra 222:7, pages 1643-1669.
Crossref
Paweł Józiak. (2018) Remarks on Hopf Images and Quantum Permutation Groups. Canadian Mathematical Bulletin 61:2, pages 301-317.
Crossref
Gastón García & Javier Gutiérrez. (2017) Quantum subgroups of simple twisted quantum groups at roots of one. Transactions of the American Mathematical Society 370:5, pages 3609-3637.
Crossref
Nicolás Andruskiewitsch & Agustín García Iglesias. (2016) Twisting Hopf algebras from cocycle deformations. ANNALI DELL'UNIVERSITA' DI FERRARA 63:2, pages 221-247.
Crossref
Xingting Wang, Xiaolan Yu & Yinhuo Zhang. (2017) Calabi–Yau property under monoidal Morita–Takeuchi equivalence. Pacific Journal of Mathematics 290:2, pages 481-510.
Crossref
Paolo Aschieri, Pierre Bieliavsky, Chiara Pagani & Alexander Schenkel. (2016) Noncommutative Principal Bundles Through Twist Deformation. Communications in Mathematical Physics 352:1, pages 287-344.
Crossref
Alex Chirvasitu & S. Paul Smith. (2017) Exotic elliptic algebras of dimension 4. Advances in Mathematics 309, pages 558-623.
Crossref
Paolo Aschieri. (2016) Deformation quantization of principal bundles. International Journal of Geometric Methods in Modern Physics 13:08, pages 1630010.
Crossref
Xiaolan Yu, Fred Van Oystaeyen & Yinhuo Zhang. (2016) Cleft extensions of Koszul twisted Calabi–Yau algebras. Israel Journal of Mathematics 214:2, pages 785-829.
Crossref
Julien Bichon & Simon Riche. (2015) Hopf algebras having a dense big cell. Transactions of the American Mathematical Society 368:1, pages 515-538.
Crossref
Kenichi Shimizu. (2015) On indicators of Hopf algebras. Israel Journal of Mathematics 207:1, pages 155-201.
Crossref
Shlomo Gelaki. (2015) Twisting of Affine Algebraic Groups, I. International Mathematics Research Notices 2015:16, pages 7552-7574.
Crossref
Zhengming Jiao & Xiaofan Zhao. (2014) Almost cocommutative and quasitriangular Hopf coquasigroups. Journal of Algebra and Its Applications 13:06, pages 1450010.
Crossref
Yunnan Li & Naihong Hu. (2014) The Green rings of the 2-rank Taft algebra and its two relatives twisted. Journal of Algebra 410, pages 1-35.
Crossref
Julien Bichon & Robert Yuncken. (2014) Quantum subgroups of the compact quantum group SU −1 (3) . Bulletin of the London Mathematical Society 46:2, pages 315-328.
Crossref
A.L. Agore & G. Militaru. (2013) Classifying complements for Hopf algebras and Lie algebras. Journal of Algebra 391, pages 193-208.
Crossref
Xiaoli Fang & Jinqi Li. (2013) Quantum Cocommutative Coalgebras in $^{H}_{H}\mathcal{YD}$ and the Solutions of the Quasi-Yang-Baxter Equation. Algebra Colloquium 20:02, pages 227-242.
Crossref
Shuangjian Guo. (2013) A METHOD TO CONSTRUCT COQUASITRIANGULAR HOPF GROUP ALGEBRAS. Asian-European Journal of Mathematics 06:01, pages 1350013.
Crossref
Pierre Guillot, Christian Kassel & Akira Masuoka. (2011) Twisting algebras using non-commutative torsors: explicit computations. Mathematische Zeitschrift 271:3-4, pages 789-818.
Crossref
ALESSANDRO ARDIZZONI, MARGARET BEATTIE & CLAUDIA MENINI. (2012) GAUGE DEFORMATIONS FOR HOPF ALGEBRAS WITH THE DUAL CHEVALLEY PROPERTY. Journal of Algebra and Its Applications 11:03, pages 1250051.
Crossref
DANIEL BULACU & STEFAAN CAENEPEEL. (2012) A MONOIDAL STRUCTURE ON THE CATEGORY OF RELATIVE HOPF MODULES. Journal of Algebra and Its Applications 11:02, pages 1250026.
Crossref
Teodor Banica, Julien Bichon & Sonia Natale. (2012) Finite quantum groups and quantum permutation groups. Advances in Mathematics 229:6, pages 3320-3338.
Crossref
Teodor Banica, Julien Bichon & Stephen Curran. (2011) Quantum automorphisms of twisted group algebras and free hypergeometric laws. Proceedings of the American Mathematical Society 139:11, pages 3961-3971.
Crossref
Tianshui Ma, Haiying Li & Shuanhong Wang. (2010) A class of new braided Hopf algebras. Frontiers of Mathematics in China 6:2, pages 293-308.
Crossref
Ma Tianshui, Li Haiying & Zhao Wenzheng. (2011) On the braided structures of Radford's biproduct. Acta Mathematica Scientia 31:2, pages 701-715.
Crossref
Georgia Benkart, Mariana Pereira & Sarah Witherspoon. (2010) Yetter–Drinfeld modules under cocycle twists. Journal of Algebra 324:11, pages 2990-3006.
Crossref
TEODOR BANICA & JULIEN BICHON. (2010) HOPF IMAGES AND INNER FAITHFUL REPRESENTATIONS. Glasgow Mathematical Journal 52:3, pages 677-703.
Crossref
Alessandro Ardizzoni, Margaret Beattie & Claudia Menini. (2010) Cocycle deformations for Hopf algebras with a coalgebra projection. Journal of Algebra 324:4, pages 673-705.
Crossref
Michihisa Wakui. (2010) Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension. Journal of Pure and Applied Algebra 214:6, pages 701-728.
Crossref
Miriam Cohen & Sara Westreich. 2010. Ring and Module Theory. Ring and Module Theory 91 114 .
Zhong-jian Lu & Xiao-li Fang. (2009) Generalized braided Hopf algebras. Applied Mathematics-A Journal of Chinese Universities 24:1, pages 105-113.
Crossref
Margaret Beattie & Daniel Bulacu. (2008) Braided Hopf Algebras Obtained from Coquasitriangular Hopf Algebras. Communications in Mathematical Physics 282:1, pages 115-160.
Crossref
Akira Masuoka. (2008) Abelian and non-abelian second cohomologies of quantized enveloping algebras. Journal of Algebra 320:1, pages 1-47.
Crossref
César Galindo & Sonia Natale. (2008) Normal Hopf subalgebras in cocycle deformations of finite groups. manuscripta mathematica 125:4, pages 501-514.
Crossref
Ju-zhen Chen, Yan Zhang & Shuan-hong Wang. (2008) Twisting theory for weak Hopf algebras. Applied Mathematics-A Journal of Chinese Universities 23:1, pages 91-100.
Crossref
Sara Westreich. (2007) Hopf Algebras of Type A n , Twistings and the FRT-construction. Algebras and Representation Theory 11:1, pages 63-82.
Crossref
Gabriella Böhm & Tomasz Brzeziński. (2007) Pre-torsors and equivalences. Journal of Algebra 317:2, pages 544-580.
Crossref
Margaret Beattie, Daniel Bulacu & Blas Torrecillas. (2007) Radford's formula for co-Frobenius Hopf algebras . Journal of Algebra 307:1, pages 330-342.
Crossref
Liang Yun Zhang. (2006) Long Bialgebras, Dimodule Algebras and Quantum Yang–Baxter Modules over Long Bialgebras. Acta Mathematica Sinica, English Series 22:4, pages 1261-1270.
Crossref
Rachel Landers, Susan Montgomery & Peter Schauenburg. (2006) Hopf powers and orders for some bismash products. Journal of Pure and Applied Algebra 205:1, pages 156-188.
Crossref
Jinqi Li. (2012) Dual Quasi-Hopf Algebras and Antipodes. Algebra Colloquium 13:01, pages 111-118.
Crossref
Miriam Cohen, Shlomo Gelaki & Sara Westreich. 2006. 173 239 .
S. Montgomery & H.-J. Schneider. (2005) Krull relations in Hopf Galois extensions: Lifting and twisting. Journal of Algebra 288:2, pages 364-383.
Crossref
Zhengming Jiao & Robert Wisbauer. (2005) The braided structures for ω-smash coproduct Hopf algebras. Journal of Algebra 287:2, pages 474-495.
Crossref
Julien Bichon. (2003) Hopf–Galois systems. Journal of Algebra 264:2, pages 565-581.
Crossref
X. Gomez & S. Majid. (2003) Braided Lie algebras and bicovariant differential calculi over co-quasitriangular Hopf algebras. Journal of Algebra 261:2, pages 334-388.
Crossref
Akira Masuoka. (2003) Cohomology and coquasi-bialgebra extensions associated to a matched pair of bialgebras. Advances in Mathematics 173:2, pages 262-315.
Crossref
Peter Schauenburg. (2002) Hopf Bimodules, Coquasibialgebras, and an Exact Sequence of Kac. Advances in Mathematics 165:2, pages 194-263.
Crossref
Yuri Bahturin, Davida Fischman & Susan Montgomery. (2001) Bicharacters, Twistings, and Scheunert's Theorem for Hopf Algebras. Journal of Algebra 236:1, pages 246-276.
Crossref
S. Montgomery. 2001. Algebra — Representation Theory. Algebra — Representation Theory 189 218 .
Peter Schauenburg. (2000) Bi-Galois objects over the Taft algebras. Israel Journal of Mathematics 115:1, pages 101-123.
Crossref
Takahiro Hayashi. (2000) Coribbon Hopf (Face) Algebras Generated by Lattice Models. Journal of Algebra 233:2, pages 614-641.
Crossref
Zhengming Jiao & Shuanhong Wang. (2000) A class of twisted braided groups. Kodai Mathematical Journal 23:1.
Crossref
Mitsuhiro Takeuchi. (1999) The Cylinder Product and Cylinder Matrices. Journal of Algebra 222:2, pages 485-499.
Crossref
Peter Schauenburg. (1999) Galois Objects over Generalized Drinfeld Doubles, with an Application to uq(sl2). Journal of Algebra 217:2, pages 584-598.
Crossref
Huixiang Chen. (1999) Skew pairing, Cocycle deformations and double crossproducts. Acta Mathematica Sinica 15:2, pages 225-234.
Crossref
Diming Lu. (1998) Monoidal functors on the category of representations of a triangular Hopf algebra. Science in China Series A: Mathematics 41:2, pages 139-146.
Crossref
Jinqi Li & Yonghua Xu. (1997) Smash coproduct and braided groups in braided monoidal category. Science in China Series A: Mathematics 40:11, pages 1121-1128.
Crossref
Andrew D. Jacobs & J. F. Cornwell. (1997) Twisting 2-cocycles for the construction of new non-standard quantum groups. Journal of Mathematical Physics 38:10, pages 5383-5401.
Crossref
Timothy J Hodges. (1997) Double Quantum Groups and Iwasawa Decomposition. Journal of Algebra 192:1, pages 303-325.
Crossref
Mitsuhiro Takeuchi. (1997) Cocycle Deformations of Coordinate Rings of Quantum Matrices. Journal of Algebra 189:1, pages 23-33.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.