We define polynomial -identities for comodule algebras over a Hopf algebra and establish general properties for the corresponding -ideals. In the case is a Taft algebra or the Hopf algebra , we exhibit a finite set of polynomial -identities which distinguish the Galois objects over up to isomorphism.
Nous définissons le concept d’identité polynomiale pour une algèbre-comodule sur une algèbre de Hopf . Nous présentons des identités polynomiales explicites distinguant à isomorphisme près les objets galoisiens d’une algèbre de Taft ou de l’algèbre de Hopf .
Keywords: Hopf algebra, comodule algebra, polynomial identity
Mot clés : algèbre de Hopf, algèbre-comodule, identité polynomiale
@article{AMBP_2013__20_2_175_0, author = {Kassel, Christian}, title = {Examples of polynomial identities distinguishing the {Galois} objects over finite-dimensional {Hopf} algebras}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {175--191}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {20}, number = {2}, year = {2013}, doi = {10.5802/ambp.325}, zbl = {1292.16024}, mrnumber = {3138028}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.325/} }
TY - JOUR AU - Kassel, Christian TI - Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras JO - Annales mathématiques Blaise Pascal PY - 2013 SP - 175 EP - 191 VL - 20 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.325/ DO - 10.5802/ambp.325 LA - en ID - AMBP_2013__20_2_175_0 ER -
%0 Journal Article %A Kassel, Christian %T Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras %J Annales mathématiques Blaise Pascal %D 2013 %P 175-191 %V 20 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.325/ %R 10.5802/ambp.325 %G en %F AMBP_2013__20_2_175_0
Kassel, Christian. Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras. Annales mathématiques Blaise Pascal, Volume 20 (2013) no. 2, pp. 175-191. doi : 10.5802/ambp.325. http://www.numdam.org/articles/10.5802/ambp.325/
[1] Simple -graded algebras and their polynomial identities, Trans. Amer. Math. Soc., to appear (arXiv:1107.4713)
[2] Graded identities of matrix algebras and the universal graded algebra, Trans. Amer. Math. Soc., Volume 362 (2010), pp. 3125-3147 | DOI | MR | Zbl
[3] Polynomial identities and noncommutative versal torsors, Adv. Math., Volume 218 (2008), pp. 1453-1495 | DOI | MR | Zbl
[4] Minimal identities for algebras, Proc. Amer. Math. Soc., Volume 1 (1950), pp. 449-463 | DOI | MR | Zbl
[5] Identities of algebras with actions of Hopf algebras, J. Algebra, Volume 202 (1998), pp. 634-654 | DOI | MR | Zbl
[6] Identities of graded algebras, J. Algebra, Volume 205 (1998), pp. 1-12 | DOI | MR | Zbl
[7] Constructing pointed Hopf algebras by Ore extensions, J. Algebra, Volume 225 (2000) no. 2, pp. 743-770 | DOI | MR | Zbl
[8] Cocharacter sequences for algebras with Hopf algebra actions, J. Algebra, Volume 185 (1996), pp. 869-885 | DOI | MR | Zbl
[9] Galois and bigalois objects over monomial non-semisimple Hopf algebras, J. Algebra Appl., Volume 5 (2006), pp. 653-680 | DOI | MR | Zbl
[10] Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras, J. Pure Appl. Algebra, Volume 204 (2006), pp. 627-665 | DOI | MR | Zbl
[11] Monomial Hopf algebras, J. Algebra, Volume 275 (2004), pp. 212-232 | DOI | MR | Zbl
[12] Quaternion algebras and Hopf crossed products, Comm. Algebra, Volume 23 (1995), pp. 3291-3325 | DOI | MR | Zbl
[13] Identities and isomorphisms of graded simple algebras, Linear Algebra Appl., Volume 432 (2010), pp. 3141-3148 | DOI | MR | Zbl
[14] Cleft extensions for a Hopf algebra generated by a nearly primitive element, Comm. Algebra, Volume 22 (1994), pp. 4537-4559 | DOI | MR | Zbl
[15] Hopf algebras and their actions on rings, Amer. Math. Soc., Providence, 1993 | MR | Zbl
[16] Cleft extensions for a class of pointed Hopf algebras constructed by Ore extensions, Comm. Algebra, Volume 29 (2001), pp. 1959-1981 | DOI | MR | Zbl
[17] Quasitriangular structures for some pointed Hopf algebras of dimension , Comm. Algebra, Volume 27 (1999), pp. 4929-4942 | DOI | MR | Zbl
[18] Polynomial identities in ring theory, Academic Press, Inc., New York–London, 1980 | MR | Zbl
[19] Hopf algebras, W. A. Benjamin, Inc., New York, 1969 | MR | Zbl
[20] The order of the antipode of finite-dimensional Hopf algebra, Proc. Nat. Acad. Sci. U.S.A., Volume 68 (1971), pp. 2631-2633 | DOI | MR | Zbl
Cited by Sources: