Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras
Quantum Algebra
2009-03-31 v1 Rings and Algebras
Abstract
Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this paper, we re-study the correspondence between left-symmetric algebras and the bijective 1-cocycles. Then a procedure is provided to classify left-symmetric algebras in terms of classification of equivalent classes of bijective 1-cocycles. As an example, the 3-dimensional complex left-symmetric algebras are classified.
Keywords
Cite
@article{arxiv.0710.2609,
title = {Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras},
author = {Chengming Bai},
journal= {arXiv preprint arXiv:0710.2609},
year = {2009}
}
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35 pages