Results 1  10
of
10
Projectivity and freeness over comodule algebras
"... Abstract. Let H be a Hopf algebra and A an Hsimple right Hcomodule algebra. It is shown that under certain hypotheses every (H,A)Hopf module is either projective or free as an Amodule and A is either a quasiFrobenius or a semisimple ring. As an application it is proved that every weakly finite ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
Abstract. Let H be a Hopf algebra and A an Hsimple right Hcomodule algebra. It is shown that under certain hypotheses every (H,A)Hopf module is either projective or free as an Amodule and A is either a quasiFrobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras, and the latter are Frobenius algebras. Similar results are obtained for Hsimple Hmodule algebras.
ON GENERALIZED HOPF GALOIS EXTENSIONS
, 2004
"... Let H be a Hopf algebra over a commutative base ring k, and A a right Hcomodule algebra with comodule structure δ: A → A ⊗ H, δ(a) =: a (0) ⊗ a (1). Denote by B:= A co H: = {b ∈ Aδ(b) = b ⊗ 1} the subalgebra of coinvariant elements. A is said to be an HGalois extension of B if the Galois map ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Let H be a Hopf algebra over a commutative base ring k, and A a right Hcomodule algebra with comodule structure δ: A → A ⊗ H, δ(a) =: a (0) ⊗ a (1). Denote by B:= A co H: = {b ∈ Aδ(b) = b ⊗ 1} the subalgebra of coinvariant elements. A is said to be an HGalois extension of B if the Galois map
Lagrange’s theorem for Hopf monoids in species
, 2012
"... Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras, ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras,
VARIETIES FOR MODULES OF QUANTUM ELEMENTARY ABELIAN GROUPS
"... Abstract. We define a rank variety for a module of a noncocommutative Hopf algebra A = Λ ⋊ G where Λ = k[X1,..., Xm]/(X ℓ 1,..., X ℓ m), G = (Z/ℓZ) m, and char k does not divide ℓ, in terms of certain subalgebras of A playing the role of “cyclic shifted subgroups”. We show that the rank variety of a ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract. We define a rank variety for a module of a noncocommutative Hopf algebra A = Λ ⋊ G where Λ = k[X1,..., Xm]/(X ℓ 1,..., X ℓ m), G = (Z/ℓZ) m, and char k does not divide ℓ, in terms of certain subalgebras of A playing the role of “cyclic shifted subgroups”. We show that the rank variety of a finitely generated module M is homeomorphic to the support variety of M defined in terms of the action of the cohomology algebra of A. As an application we derive a theory of rank varieties for the algebra Λ. When ℓ = 2, rank varieties for Λmodules were constructed by Erdmann and Holloway using the representation theory of the Clifford algebra. We show that the rank varieties we obtain for Λmodules coincide with those of Erdmann and Holloway. 1.
unknown title
, 2006
"... Projectivity of Hopf algebras over subalgebras with semilocal central localizations ..."
Abstract
 Add to MetaCart
Projectivity of Hopf algebras over subalgebras with semilocal central localizations
Invariants of finite Hopf algebras
, 2002
"... This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings. Suppose that H is a finite dimensional Hopf algebra and A a commutative algebra, say over a field K. Let δ: A → A ⊗ H be an algebra homo ..."
Abstract
 Add to MetaCart
This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings. Suppose that H is a finite dimensional Hopf algebra and A a commutative algebra, say over a field K. Let δ: A → A ⊗ H be an algebra homomorphism which makes
MODULE CATEGORIES OVER POINTED HOPF ALGEBRAS
, 811
"... Abstract. We develop some techniques to the study of exact module categories over some families of pointed finitedimensional Hopf algebras. As an application we classify exact module categories over the tensor ..."
Abstract
 Add to MetaCart
Abstract. We develop some techniques to the study of exact module categories over some families of pointed finitedimensional Hopf algebras. As an application we classify exact module categories over the tensor
TABLE OF CONTENTS ACKNOWLEDGEMENTS..............................
"... On Hopf algebras of dimension 4p by YiLin Cheng ..."