Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras

Details Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras

2007-10-13

arxiv.org/abs/0710.2609v1

Communications in Algebra 37 (2009) 1016-1057

Mathematics

Quantum Algebra

35 pages

Scientific paper

10.1080/00927870802279030

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.

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