Simple graded commutative algebras

被引：16

作者：

Morier-Genoud, Sophie ^{[2
]}

Ovsienko, Valentin ^{[1
]}

机构：

[1] Univ Lyon 1, CNRS, Inst Camille Jordan, F-69622 Villeurbanne, France

[2] Univ Paris 07, UFR Math Case 7012, F-75205 Paris 13, France

来源：

JOURNAL OF ALGEBRA | 2010年 / 323卷 / 06期

关键词：

Graded commutative algebra; Clifford algebras; OCTONIONS; GRADINGS;

D O I：

10.1016/j.jalgebra.2010.01.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the notion of Gamma-graded commutative algebra for an arbitrary abelian groLip Gamma. The main examples are the Clifford algebras already treated in H. Albuquerque and S. Majid (2002) [2]. We prove that the Clifford algebras are the only simple finite-dimensional associative graded commutative algebras over R or C. Our approach also leads to non-associative graded commutative algebras extending the Clifford algebras. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1649 / 1664

页数：16

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