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Original Articles

Braided Enveloping Algebras Associated to Quantum Parabolic Subalgebras

Pages 3491-3514 | Received 21 Aug 2009, Published online: 14 Oct 2011

REFERENCES

  • Andruskiewitsch , N. ( 2004 ). Some remarks on Nichols algebras . In: Hopf Algebras. Vol. 237 , New York : Dekker , pp. 35 – 45 .
  • Andruskiewitsch , N. , Schneider , H.-J. ( 2000 ). Finite quantum groups and Cartan matrices . Adv. Math. 154 ( 1 ): 1 – 45 .
  • Andruskiewitsch , N. , Schneider , H.-J. ( 2002 ). Pointed Hopf algebras . In: New Directions in Hopf Algebras . Vol. 43 , Cambridge : Cambridge, Univ. Press , pp. 1 – 68 .
  • Andruskiewitsch , N. , Schneider , H.-J. ( 2010 ). On the classification of finite-dimensional pointed Hopf algebras . Ann. of Math. 171 ( 1 ): 375 – 417 .
  • Brown , K. A. , Goodearl , K. R. (2002). Lectures on algebraic quantum groups . Basel : Birkhäuser Verlag.
  • De Concini , C. , Lyubashenko , V. ( 1994 ). Quantum function algebra at roots of 1 . Adv. Math. 108 ( 2 ): 205 – 262 .
  • Drinfel'd , V. G. ( 1985 ). Hopf algebras and the quantum Yang-Baxter equation . Dokl. Akad. Nauk SSSR 283 ( 5 ): 1060 – 1064 .
  • Drinfel'd , V. G. ( 1987 ). Quantum groups. Proceedings of the international congress of mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), pp. 798–820. Providence, RI: Amer. Math. Soc .
  • GAP-Groups, Algorithms, and Programming, Version 4.4. (2011). at http://www.gap-system.org/ .
  • Grabowski , J. E. ( 2005 ). On Lie induction and the exceptional series . J. Algebra Appl. 4 ( 6 ): 707 – 737 . (Special Issue on Representation Theory and Its Applications.)
  • Grabowski , J. E. ( 2006 ). Inductive constructions for Lie bialgebras and Hopf algebras. Unpublished doctoral dissertation, University of London .
  • Grabowski , J. E. ( 2008 ). Braided-Lie bialgebras associated to Kac-Moody algebras . J. Lie Theory 18 ( 1 ): 125 – 140 .
  • Jantzen , J. C. ( 1996 ). Lectures on quantum groups Vol. 6. Providence, RI: American Mathe- matical Society .
  • Jimbo , M. ( 1985 ). A q-difference analogue of U(g) and the Yang-Baxter equation . Lett. Math. Phys. 10 ( 1 ): 63 – 69 .
  • Joseph , A. ( 1995 ). Quantum Groups and Their Primitive Ideals . Vol. 29 . Berlin : Springer-Verlag .
  • Kac , V. G. ( 1990 ). Infinite-Dimensional Lie Algebras. , 3rd ed. Cambridge : Cambridge University Press .
  • Kolb , S. ( 2008 ). The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weight . J. Algebra 319 ( 8 ): 3518 – 3534 .
  • Lusztig , G. ( 1993 ). Introduction to Quantum Groups . Vol. 110 . Boston , MA : Birkhauser Boston Inc .
  • Mac Lane , S. ( 1998 ). Categories for the Working Mathematician. , 2nd ed. Vol. 5 . New York : Springer-Verlag .
  • Majid , S. ( 1990 ). More examples of bicrossproduct and double cross product Hopf algebras . Israel J. Math. 72 ( 1-2 ): 133 – 148 .
  • Majid , S. ( 1993 ). Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group . Comm. Math. Phys. 156 ( 3 ): 607 – 638 .
  • Majid , S. ( 1994 ). Cross products by braided groups and bosonization . J. Algebra 163 ( 1 ): 165 – 190 .
  • Majid , S. ( 1995 ). Foundations of Quantum Group Theory . Cambridge : Cambridge University Press .
  • Majid , S. ( 1997a ). Braided geometry and the inductive construction of Lie algebras and quantum groups . In: Deformation theory and symplectic geometry (ascona, 1996) Vol. 20 , pp. 339 – 344 . Dordrecht : Kluwer Acad. Publ.
  • Majid , S. ( 1997b ). New quantum groups by double-bosonisation . Czechoslovak J. Phys. 47 ( 1 ): 79 – 90 . (Quantum groups and integrable systems, II (Prague, 1996))
  • Majid , S. ( 1999 ). Double-bosonisation of braided groups and the construction of Uq(g) . Math. Proc. Cambridge Philos. Soc. 125 ( 1 ): 151 – 192 .
  • Majid , S. ( 2000 ). Braided-Lie bialgebras . Pacific J. Math. 192 ( 2 ): 329 – 356 .
  • Majid , S. ( 2002 ). A Quantum Groups Primer (No. 292). Cambridge: Cambridge University Press .
  • Nichols , W. D. ( 1978 ). Bialgebras of type one . Comm. Algebra 6 ( 15 ): 1521 – 1552 .
  • Radford , D. E. ( 1985 ). The structure of Hopf algebras with a projection . J. Algebra 92 ( 2 ): 322 – 347 .
  • Robinson , D. J. S. (1996). A Course in the Theory of Groups. , 2nd ed. Vol. 80 . New York : Springer-Verlag.
  • Rosso , M. ( 1998 ). Quantum groups and quantum shuffles . Invent. Math. 133 ( 2 ): 399 – 416 .
  • Sommerhäuser , Y. ( 1996 ). Deformed enveloping algebras . New York J. Math. 2 : 35 – 58 , electronic .
  • Takeuchi , M. ( 2005 ). A survey on Nichols algebras . In: Algebraic structures and their represen- tations Vol. 376 , Providence , RI : Amer. Math. Soc. pp. 105 – 117 .
  • Ufer , S. ( 2004a ). Nichols algebras of U q (𝔤)-modules. Preprint, arXiv:math/0403282 .
  • Ufer , S. ( 2004b ). PBW bases for a class of braided Hopf algebras . J. Algebra 280 ( 1 ): 84 – 119 .
  • Woronowicz , S. L. ( 1989 ). Differential calculus on compact matrix pseudogroups (quantum groups) . Comm. Math. Phys. 122 ( 1 ): 125 – 170 .
  • Communicated by T. Lenagan.

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