1302.5776 (Run-Xuan Zhang)

Left-symmetric Structures on Complex Simple Lie Superalgebras    [PDF]

Run-Xuan Zhang

A well-known fact is that there does not exist any compatible left-symmetric structures on a finite-dimensional complex semisimple Lie algebra (see \cite{Chu1974}). 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 $A(m,n)(m\neq n)$ and Cartan simple Lie superalgebra $W(n)(n\geq 3)$. We also classify all compatible LSSAs with a right-identity on A(0,1).

View original: http://arxiv.org/abs/1302.5776