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
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
收藏
页码:1649 / 1664
页数:16
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