منابع مشابه
The Grothendieck Group of Hopf Algebras
Let H be a cosemisimple Hopf algebra over an algebraically closed field k. Assume that H contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with order 2 or 3, a Hopf subalgebra of dimension 75, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. I...
متن کاملOn the Grothendieck Ring of a Hopf Algebra
• The Grothendieck ring G0(H) is the abelian group generated by the iso. classes [V ] of finite dim’l (right) H-modules V modulo the relations [V ] = [U ] + [W ] for each s.e.s. 0 → U → V → W → 0. The iso. classes of simple modules form a Z-basis. Multiplication is given by ⊗ = ⊗k. • The character algebra R(H) is the k-subalgebra of H∗ that is generated by the image of the character map χ : G0(...
متن کاملThe Hopf Algebra of a Uniserial Group
Let k be an algebraically closed field of characteristic p > 0. The purpose of this paper is to describe the Hopf algebra of a finite commutative infinitesimal unipotent k-group scheme which is uniserial, i.e., which has a unique composition series. As there is only one simple finite commutative infinitesimal unipotent group scheme (namely αp := ker {F : Ga → Ga} , with Ga being the additive gr...
متن کاملThe Brauer Group of a Hopf Algebra
Let H be a Hopf algebra with a bijective antipode over a commutative ring k with unit. The Brauer group of H is defined as the Brauer group of Yetter–Drinfel’d H-module algebras, which generalizes the Brauer–Long group of a commutative and cocommutative Hopf algebra and those known Brauer groups of structured algebras.
متن کاملAn Isomorphism for the Grothendieck Ring of a Hopf Algebra Order
If G is a finite abelian group, R is a principal ideal domain with field of quotients an algebraic number field K which splits G, and if A is a Hopf algebra order in KG, then the Grothendieck ring of the category of finitely generated A-modules is isomorphic to the Grothendieck ring of the category of finitely generated RG-modules. The Grothendieck group a£ of the category of finitely generated...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1996
ISSN: 0022-4049
DOI: 10.1016/0022-4049(95)00023-2