The cohomology of left-symmetric conformal algebra and its applications

2022/10/02 by Jun Zhao, Bo Hou, Zhao, Jun +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2210.00466

openalex publication_date 2022/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces of the left-symmetric conformal algebra and its sub-adjacent Lie conformal algebra. As applications of the cohomology theory, we study linear deformations, formal 1-parameter deformations, T^*-extensions of a left-symmetric conformal algebra respectively and obtain some properties.

Related

• Classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra W(a,b)
• Cohomology and derivations of BiHom-Lie conformal algebras
• Cohomologies and Deformations of Generalized Left-symmetric Algebras
• The construction of Hom left-symmetric conformal bialgebras
• Algebraic constructions for left-symmetric conformal algebras