共查询到10条相似文献,搜索用时 62 毫秒
1.
We prove that, if H is a finite-dimensional semisimple Hopf algebra, and A is an FCR H-module algebra over an algebraically closed field, then A is a PI-algebra, provided the subalgebra of invariants is a PI-algebra. We also show that if A is an affine algebra with an action of a finite group G by automorphisms, the subalgebra of the fixed points A G is in the center of A, and the characteristic of the ground field is either zero or relatively prime to the order of G, then A G is affine. Analogous results are proved for graded algebras and H-module algebras over a semisimple triangular Hopf algebra over a field of characteristic zero. We prove also that, if A is an H-module algebra with an identity element, and H is either a semisimple group algebra or its dual, then, if A is semiprimitive (semiprime), then so is A H. 相似文献
2.
In this paper we study the isotypic decomposition of the regular module of a finite-dimensional Hopf algebra over an algebraically closed field of characteristic zero. For a semisimple Hopf algebra, the idempotents realizing the isotypic decomposition can be explicitly expressed in terms of characters and the Haar integral. In this paper we investigate Hopf algebras with the Chevalley property, which are not necessarily semisimple. We find explicit expressions for idempotents in terms of Hopf-algebraic data, where the Haar integral is replaced by the regular character of the dual Hopf algebra. For a large class of Hopf algebras, these are shown to form a complete set of orthogonal idempotents. We give an example which illustrates that the Chevalley property is crucial. 相似文献
3.
V. A. Artamonov and I. A. Chubarov proved a criterion under which an element of some semisimple finite-dimensional Hopf algebra
is group-like. The studied Hopf algebra has only one nonone- dimensional irreducible representation. Let n be a dimension of this representation. It is shown in this paper that for odd prime n the set of group-like elements of these algebras is a cyclic group of order 2 n. 相似文献
4.
The paper is concerned with the semisimplicity of smash products of quasitriangular weak Hopf algebras. Let ( H, R) be a finite dimensional quasitriangular weak Hopf algebra over a field k and A any semisimple and quantum commutative weak H-module algebra. Based on the work of Nikshych et al. (Topol. Appl. 127(1–2):91–123, 2003), we give Maschke’s theorem for smash products of quasitriangular weak Hopf algebras, stating that A# H is semisimple if and only if A is a projective left A# H-module, which extends the Theorem 3.2 given in Yang and Wang (Commun. Algebra 27(3):1165–1170, 1999). 相似文献
5.
Depth one extensions of finite dimensional semisimple algebras are completely characterized in terms of their algebra centers. For extensions of semisimple Hopf algebras this characterization translates into a trivial monoidal action of the dual fusion category Rep( A *) on Rep( B). 相似文献
6.
We extend the Larson–Sweedler theorem [Amer. J. Math. 91 (1969) 75] to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf algebra is autonomous monoidal with semisimple unit and invertible modules. We also reveal the connection of invertible modules to left and right grouplike elements in the dual weak Hopf algebra. Defining distinguished left and right grouplike elements, we derive the Radford formula [Amer. J. Math. 98 (1976) 333] for the fourth power of the antipode in a weak Hopf algebra and prove that the order of the antipode is finite up to an inner automorphism by a grouplike element in the trivial subalgebra AT of the underlying weak Hopf algebra A. 相似文献
7.
Let H be a Hopf algebra over the field k which is a finite module over a central affine sub-Hopf algebra R. Examples include enveloping algebras of finite dimensional k-Lie algebras in positive characteristic and quantised enveloping algebras and quantised function algebras at roots of unity. The ramification
behaviour of the maximal ideals of Z( H) with respect to the subalgebra R is studied, and the conclusions are then applied to the cases of classical and quantised enveloping algebras. In the case
of for semisimple a conjecture of Humphreys [28] on the block structure of is confirmed. In the case of for semisimple and an odd root of unity we obtain a quantum analogue of a result of Mirković and Rumynin, [35], and we fully describe the factor
algebras lying over the regular sheet, [9]. The blocks of are determined, and a necessary condition (which may also be sufficient) for a baby Verma -module to be simple is obtained.
Received: 24 June 1999; in final form: 30 March 2000 / Published online: 17 May 2001 相似文献
8.
ABSTRACT Starting from a Hopf algebra endowed with an action of a group π by Hopf automorphisms, we construct (by a “twisted” double method) a quasitriangular Hopf π-coalgebra. This method allows us to obtain non-trivial examples of quasitriangular Hopf π-coalgebras for any finite group π and for infinite groups π such as GL n ( 𝕂). In particular, we define the graded quantum groups, which are Hopf π-coalgebras for π = ?[[ h]] l and generalize the Drinfeld-Jimbo quantum enveloping algebras. 相似文献
9.
We obtain further classification results for semisimple Hopf algebras of dimension pq
2 over an algebraically closed field k of characteristic zero. We complete the classification of semisimple Hopf algebras of dimension 28. 相似文献
10.
Let m be a positive integer, not divisible by 2, 3, 5, 7. We generalize the classification of basic quasi-Hopf algebras over cyclic groups of prime order given in Etingof and Gelaki (2006) [11] to the case of cyclic groups of order m. To this end, we introduce a family of non-semisimple radically graded quasi-Hopf algebras A( H, s), constructed as subalgebras of Hopf algebras twisted by a quasi-Hopf twist, which are not twist equivalent to Hopf algebras. Any basic quasi-Hopf algebra over a cyclic group of order m is either semisimple, or is twist equivalent to a Hopf algebra or a quasi-Hopf algebra of type A( H, s). 相似文献
|