Graded semisimple algebras are symmetric

被引：1

作者：

Dascalescu, S. ^{[1
,2
]}

Nastasescu, C. ^{[1
,3
]}

Nastasescu, L. ^{[1
,3
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, Str Acad 14, RO-010014 Bucharest 1, Romania

[2] Univ Bucharest, ICUB, Bucharest, Romania

[3] Romanian Acad, Inst Math, POB 1-764, RO-014700 Bucharest, Romania

来源：

JOURNAL OF ALGEBRA | 2017年 / 491卷

关键词：

Graded algebra; Frobenius algebra; Symmetric algebra; Graded division algebra; Crossed product; Graded semisimple algebra; FROBENIUS ALGEBRAS;

D O I：

10.1016/j.jalgebra.2017.08.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded semisimple algebra is graded symmetric. The center of a symmetric algebra is not necessarily symmetric, but we prove that the center of a finite dimensional graded division algebra is symmetric, provided that the order of the grading group is not divisible by the characteristic of the base field. (c) 2017 Elsevier Inc. All rights reserved.

引用

页码：207 / 218

页数：12

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