|
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 8, Pages 14–22
(Mi ivm7861)
|
|
|
|
This article is cited in 5 scientific papers (total in 5 papers)
Invariants of the action of a semisimple finite-dimensional Hopf algebra on special algebras
M. S. Eryashkin Chebotarev Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Russia
Abstract:
In this paper we extend classical results of the invariant theory of finite groups to the action of a finite-dimensional semisimple Hopf algebra $H$ on a special algebra $A$, which is homomorphically mapped onto a commutative integral domain, and the kernel of this map contains no nonzero $H$-stable ideal. We prove that the algebra $A$ is finitely generated as a module over a subalgebra of invariants, and the latter is finitely generated as a $\mathbf k$-algebra. We give a counterexample for the finite generation of a non-semisimple Hopf algebra.
Keywords:
Hopf algebras, invariant rings.
Received: 20.05.2010
Citation:
M. S. Eryashkin, “Invariants of the action of a semisimple finite-dimensional Hopf algebra on special algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 8, 14–22; Russian Math. (Iz. VUZ), 55:8 (2011), 11–18
Linking options:
https://www.mathnet.ru/eng/ivm7861 https://www.mathnet.ru/eng/ivm/y2011/i8/p14
|
Statistics & downloads: |
Abstract page: | 302 | Full-text PDF : | 90 | References: | 42 | First page: | 3 |
|