Left-symmetric Structures on Complex Simple Lie Superalgebras

2013/02/23 by Run-Xuan Zhang, Zhang, Run-Xuan
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Lie group #Mathematical Physics (math-ph) #Mathematics #Philosophy #Pure mathematics #Rings and Algebras (math.RA) #Simple (philosophy) #Simple Lie group #math-ph #math.MP #math.RA

paper · pdf · doi:10.48550/arxiv.1302.5776

arxiv created 2013/02/23 · openalex publication_date 2013/02/23 · arxiv updated 2013/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A well-known fact is that there does not exist any compatible left-symmetric structures on a finite-dimensional complex semisimple Lie algebra (see \citeChu1974). This result is not valid in semisimple Lie superalgebra case. In this paper, we study the compatible Left-symmetric superalgebra (LSSA for short) structures on complex simple Lie superalgebras. We prove that there is not any compatible LSSA structure on a finite-dimensional complex simple Lie superalgebra except for the classical simple Lie superalgebra A(m,n)(m≠ n) and Cartan simple Lie superalgebra W(n)(n≥ 3). We also classify all compatible LSSAs with a right-identity on A(0,1).

Citations

• The Cohomology Structure of an Associative Ring

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