Actions of cocommutative Hopf algebras

JOURNAL OF ALGEBRA

卷:546

Article

Lorenz, Martin¹  Nguyen, Bach¹  Yammine, Ramy¹ 

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

关键词: Hopf algebra;    Action;    Quantum invariant theory;    Prime spectrum;    Stratification;    Prime ideal;    Semiprime ideal;    Integral action;    Rational action;    Algebraic group;    Lie algebra;    Derivation;   

DOI  :  10.1016/j.jalgebra.2019.11.010

来源: Elsevier

【 摘 要 】

Let H be a cocommutative Hopf algebra acting on an algebra A. Assuming the base field to be algebraically closed and the H-action on A to be integral, that is, it is given by a coaction of some Hopf subalgebra of the finite dual H degrees that is an integral domain, we stratify the prime spectrum Spec A in terms of the prime spectra of certain commutative algebras. For arbitrary H-actions in characteristic 0, we show that the largest H-stable ideal of A that is contained in a given semiprime ideal of A is semiprime as well. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free