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

35 pages

References in corpus (2)

• Field Algebras
• A Unified Algebraic Approach to Classical Yang-Baxter Equation

Cited by in corpus (6)

• The algebraic and geometric classification of nilpotent left-symmetric algebras
• Some Non-Abelian Phase Spaces in Low Dimensions
• Left-symmetric Superalgebras on Special Linear Lie Superalgebras
• Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2
• Cohomology of left-symmetric color algebras
• Kupershmidt-Nijenhuis structures on pre-Malcev algebras