Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras
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- by Uma N. Iyer and Christian Kassel PDF
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Abstract:
After recalling the definitions and the properties of the generic base algebra and of the universal comodule algebra attached to a Hopf algebra given by Aljadeff and the second-named author, we determine these algebras for the Taft algebras, the Hopf algebras $E(n)$ and certain monomial Hopf algebras.References
- Eli Aljadeff, Darrell Haile, and Michael Natapov, Graded identities of matrix algebras and the universal graded algebra, Trans. Amer. Math. Soc. 362 (2010), no. 6, 3125–3147. MR 2592949, DOI 10.1090/S0002-9947-10-04811-7
- Eli Aljadeff and Christian Kassel, Polynomial identities and noncommutative versal torsors, Adv. Math. 218 (2008), no. 5, 1453–1495. MR 2419929, DOI 10.1016/j.aim.2008.03.014
- M. Beattie, S. Dăscălescu, and L. Grünenfelder, Constructing pointed Hopf algebras by Ore extensions, J. Algebra 225 (2000), no. 2, 743–770. MR 1741560, DOI 10.1006/jabr.1999.8148
- Julien Bichon, Galois and bigalois objects over monomial non-semisimple Hopf algebras, J. Algebra Appl. 5 (2006), no. 5, 653–680. MR 2269410, DOI 10.1142/S0219498806001934
- Julien Bichon and Giovanna Carnovale, Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras, J. Pure Appl. Algebra 204 (2006), no. 3, 627–665. MR 2185622, DOI 10.1016/j.jpaa.2005.06.002
- Xiao-Wu Chen, Hua-Lin Huang, Yu Ye, and Pu Zhang, Monomial Hopf algebras, J. Algebra 275 (2004), no. 1, 212–232. MR 2047446, DOI 10.1016/j.jalgebra.2003.12.019
- Christian Kassel, Generic Hopf Galois extensions, Quantum groups and noncommutative spaces, Aspects Math., E41, Vieweg + Teubner, Wiesbaden, 2011, pp. 104–120. MR 2798437, DOI 10.1007/978-3-8348-9831-9_{6}
- C. Kassel, Hopf algebras and polynomial identities, Proc. Conf. “Quantum Groups and Quantum Topology”, RIMS, Kyoto University, April 2010, RIMS Kôkyûroku 1714, 2010, 49–62, arXiv:1009.3180.
- Christian Kassel and Akira Masuoka, Flatness and freeness properties of the generic Hopf Galois extensions, Rev. Un. Mat. Argentina 51 (2010), no. 1, 79–94. MR 2681260
- Susan Montgomery, Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, vol. 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993. MR 1243637, DOI 10.1090/cbms/082
- Florin Panaite and Freddy Van Oystaeyen, Quasitriangular structures for some pointed Hopf algebras of dimension $2^n$, Comm. Algebra 27 (1999), no. 10, 4929–4942. MR 1701714, DOI 10.1080/00927879908826739
- Louis Halle Rowen, Polynomial identities in ring theory, Pure and Applied Mathematics, vol. 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 576061
- Mitsuhiro Takeuchi, Free Hopf algebras generated by coalgebras, J. Math. Soc. Japan 23 (1971), 561–582. MR 292876, DOI 10.2969/jmsj/02340561
Additional Information
- Uma N. Iyer
- Affiliation: Department of Mathematics and Computer Science, Bronx Community College, 2155 University Avenue, Bronx, New York 10453
- Email: uma.iyer@bcc.cuny.edu
- Christian Kassel
- Affiliation: Institut de Recherche Mathématique Avancée, CNRS and Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France
- ORCID: 0000-0003-2580-1608
- Email: kassel@math.unistra.fr
- Received by editor(s): June 17, 2013
- Received by editor(s) in revised form: September 17, 2013, and September 23, 2013
- Published electronically: April 9, 2015
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 8465-8486
- MSC (2010): Primary 16R50, 16T05, 16T15
- DOI: https://doi.org/10.1090/tran/6287
- MathSciNet review: 3403062