Classifying complements for associative algebras

被引：7
|
作者：
Agore, A. L. [1 ,2 ]
机构：
[1] Vrije Univ Brussel, Fac Engn, B-1050 Brussels, Belgium
[2] Bucharest Univ Econ Studies, Dept Appl Math, RO-010374 Bucharest 1, Romania
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 446卷
关键词：
Classifying complements problem; Matched pair of algebras; HOPF-ALGEBRAS; MATCHED PAIRS; CONSTRUCTION; PRODUCTS;
D O I：
10.1016/j.laa.2014.01.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a given extension A subset of E of associative algebras we describe and classify up to an isomorphism all A-complements of E, i.e. all subalgebras X of E such that E = A + X and A boolean AND X = {0}. Let X be a given complement and (A, X, , <-, -> the canonical matched pair associated with the factorization E = A + X. We introduce a new type of deformation of the algebra X by means of the given matched pair and prove that all A-complements of E are isomorphic to such a deformation of X. Several explicit examples involving the matrix algebra are provided. (C) 2014 Elsevier Inc. All rights reserved.
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页码：345 / 355
页数：11
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