Determinants, integrality and Noether's theorem for quantum commutative algebras

Miriam Cohen; Sara Westreich; Shenglin Zhu

doi:10.1007/BF02785538

Determinants, integrality and Noether's theorem for quantum commutative algebras

Miriam Cohen, Sara Westreich, Shenglin Zhu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The aim of this paper is to generalize Noether's theorem for finite groups acting on commutative algebras, to finite-dimensional triangular Hopf algebras acting on quantum commutative algebras. In the process we construct a non-commutative determinant function which yields an analogue of the Cayley-Hamilton theorem for certain endomorphisms.

Original language	English
Pages (from-to)	185-222
Number of pages	38
Journal	Israel Journal of Mathematics
Volume	96
DOIs	https://doi.org/10.1007/BF02785538
State	Published - 1 Jan 1996

ASJC Scopus subject areas

General Mathematics

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title = "Determinants, integrality and Noether's theorem for quantum commutative algebras",

abstract = "The aim of this paper is to generalize Noether's theorem for finite groups acting on commutative algebras, to finite-dimensional triangular Hopf algebras acting on quantum commutative algebras. In the process we construct a non-commutative determinant function which yields an analogue of the Cayley-Hamilton theorem for certain endomorphisms.",

author = "Miriam Cohen and Sara Westreich and Shenglin Zhu",

year = "1996",

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AU - Cohen, Miriam

AU - Westreich, Sara

AU - Zhu, Shenglin

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N2 - The aim of this paper is to generalize Noether's theorem for finite groups acting on commutative algebras, to finite-dimensional triangular Hopf algebras acting on quantum commutative algebras. In the process we construct a non-commutative determinant function which yields an analogue of the Cayley-Hamilton theorem for certain endomorphisms.

AB - The aim of this paper is to generalize Noether's theorem for finite groups acting on commutative algebras, to finite-dimensional triangular Hopf algebras acting on quantum commutative algebras. In the process we construct a non-commutative determinant function which yields an analogue of the Cayley-Hamilton theorem for certain endomorphisms.

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DO - 10.1007/BF02785538

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SP - 185

EP - 222

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Determinants, integrality and Noether's theorem for quantum commutative algebras

Abstract

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