Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 68, 2020 - Issue 1
Submit an article Journal homepage
111
Views
5
CrossRef citations to date
0
Altmetric
Articles

Rota-type operators on null-filiform associative algebras

Iqboljon KarimjanovDepartment of Matemáticas, Institute of Matemáticas, University of Santiago de Compostela, Santiago de Compostela, SpainView further author information
,
Ivan KaygorodovCMCC, Universidade Federal do ABC, Santo André, BrasilCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0003-2084-9215View further author information
ORCID Icon &
Manuel LadraDepartment of Matemáticas, Institute of Matemáticas, University of Santiago de Compostela, Santiago de Compostela, SpainView further author information
Pages 205-219 | Received 05 Jun 2018, Accepted 12 Jul 2018, Published online: 01 Aug 2018

References

  • Rota GC. Baxter operators, an introduction. In: Joseph PS Kung, editor, Gian-Carlo Rota on combinatorics, introductory papers and commentaries. Boston: Birkhäuser; 1995.
  • Gao X, Guo L. Rota's classification problem, rewriting systems and Gröbner-Shirshov bases. J Algebra. 2017;470:219–253. doi: 10.1016/j.jalgebra.2016.09.006
  • Guo L. An introduction to Rota–Baxter Algebra. US, China: International Press and Higher Education Press; 2012.
  • Pan Y, Liu Q, Bai C, et al. PostLie algebra structures on the Lie algebra sl(2,C). Electron J Linear Algebra. 2012;23:180–197.
  • Pei J, Bai C, Guo L. Rota–Baxter operators on sl(2,C) and solutions of the classical Yang-Baxter equation. J Math Phys. 2014;55(2):021701. 17 pp. doi: 10.1063/1.4863898
  • Tang X, Zhang Y, Sun Q. Rota–Baxter operators on 4-dimensional complex simple associative algebras. Appl Math Comput. 2014;229:173–186.
  • Benito P, Gubarev V, Pozhidaev A. Rota–Baxter operators on quadratic algebras, arXiv:1801.07037
  • Guo L, Liu Z. Rota–Baxter operators on generalized power series rings. J Algebra Appl. 2009;8(4):557–564. doi: 10.1142/S0219498809003515
  • Mazurek R. Rota–Baxter operators on skew generalized power series rings. J Algebra Appl. 2014;13(7):1450048. 10 pp. doi: 10.1142/S0219498814500480
  • Yu H. Classification of monomial Rota–Baxter operators on k[x]. J Algebra Appl. 2016;15(5):1650087. 16 pp.. doi: 10.1142/S0219498816500870
  • Zheng S, Guo L, Rosenkranz M. Rota–Baxter operators on the polynomial algebra, integration, and averaging operators. Pacific J Math. 2015;275(2):481–507. doi: 10.2140/pjm.2015.275.481
  • Gao X, Liu M, Bai C, et al. Rota–Baxter operators on Witt and Virasoro algebras. J Geom Phys. 2016;108:1–20. doi: 10.1016/j.geomphys.2016.06.007
  • Bai R, Zhang Y. Homogeneous Rota–Baxter operators on the 3-Lie algebra Aω. Colloq Math. 2017;148(2):195–213. doi: 10.4064/cm6829-2-2016
  • Bai R, Zhang Y. Homogeneous Rota–Baxter operators on the 3-Lie algebra Aω (II). Colloq Math. 2017;149(2):193–209. doi: 10.4064/cm7000-4-2017
  • Bahturin Yu., Goze M, Remm E. Group gradings on filiform Lie algebras. Comm Algebra. 2016;44(1):40–62. doi: 10.1080/00927872.2014.937535
  • Draper C, Martín C. Gradings on the Albert algebra and on f4. Rev Mat Iberoam. 2009;25(3):841–908.
  • Elduque A. Fine gradings on simple classical Lie algebras. J Algebra. 2010;324(12):3532–3571. doi: 10.1016/j.jalgebra.2010.09.018
  • Patera J, Zassenhaus H. On Lie gradings I. Linear Algebra Appl. 1989;112:87–159. doi: 10.1016/0024-3795(89)90591-0
  • Chaves M, Singleton D. Phantom energy from graded algebras. Modern Phys Lett A. 2007;22(1):29–40. doi: 10.1142/S0217732307022372
  • Verbovetsky A. Lagrangian formalism over graded algebras. J Geom Phys. 1996;18(3):195–214. doi: 10.1016/0393-0440(95)00017-8
  • Jurco B. From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets. J Geom Phys. 2012;62(12):2389–2400. doi: 10.1016/j.geomphys.2012.09.002
  • Khudoyberdiyev A, Omirov B. Infinitesimal deformations of naturally graded filiform Leibniz algebras. J Geom Phys. 2014;86:149–163. doi: 10.1016/j.geomphys.2014.07.034
  • Dekimpe K, Ongenae V. Filiform left-symmetric algebras. Geom Dedicata. 1999;74(2):165–200. doi: 10.1023/A:1005004223336
  • Liu X, Guo L, Guo X. λ-Differential operators and λ-differential modules for the Virasoro algebra. Linear Multilinear Algebra. 2018. DOI: 10.1080/03081087.2018.1451479

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.