منابع مشابه
Duals of Pointed Hopf Algebras
In this paper, we study the duals of some finite dimensional pointed Hopf algebras working over an algebraically closed field k of characteristic 0. In particular, we study pointed Hopf algebras with coradical k[Γ] for Γ a finite abelian group, and with associated graded Hopf algebra of the form B(V )#k[Γ] where B(V ) is the Nichols algebra of V = ⊕iV χi gi ∈ k[Γ] k[Γ]YD. As a corollary to a ge...
متن کاملActions of Pointed Hopf Algebras
Definition 1.2 The invariants of H in A is the set A of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforvard computations shows, that A is the subalgebra of A. We refer reader to [5], [6] for the basic information concerning Hopf algebras and their actions on associative algebras. As a generalization of the well-known fact for group actions the following question raised in [5] ( Questio...
متن کاملGeneralized Path Algebras and Pointed Hopf Algebras
Most of pointed Hopf algebras of dimension p with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras it is obtained that the representations, homological dimensions and radicals of these Hopf algebras. The relations between the radicals of path algebras and connectivity of directed graphs are given. 2000 Mathematics subject Classification: 16w3...
متن کاملCohomology of Finite Dimensional Pointed Hopf Algebras
We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig’s small quantum groups, whose cohomology was first computed explicitly by Gin...
متن کاملHopf Algebras of Dimension
Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integers n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd primes p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some pro...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2000
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870008827002