ON GRADED ASSOCIATIVE ALGEBRAS

被引：13
|
作者：
Martin, Antonio J. Calderon [1 ]
机构：
[1] Univ Cadiz, Dept Matemat, Cadiz 11510, Spain
来源：
REPORTS ON MATHEMATICAL PHYSICS | 2012年 / 69卷 / 01期
关键词：
graded algebra; associative algebra; structure theory; GROUP GRADINGS; FINE GRADINGS; LIE GRADINGS; GEOMETRY;
D O I：
10.1016/S0034-4877(12)60018-4
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Consider 21 an associative algebra of arbitrary dimension and over an arbitrary base field K, graded by means of an abelian group G. We show that 21 is of the form 21 U + Sigma(j) I-j with U a linear subspace of 21(1) and any I-j a well described graded ideal of 21, satisfying I-j I-k = 0 if j not equal k. Under certain conditions, the simplicity of 21 is characterized and it is shown that 21 is the direct sum of the family of its minimal graded ideals, each one being a simple graded associative algebra.
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页码：75 / 86
页数：12
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