Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras

Iyer, Uma; Kassel, Christian

doi:10.1090/tran/6287

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

Trans. Amer. Math. Soc. 367 (2015), 8465-8486 Request permission

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