English

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}
}

Comments

35 pages