Classification of finite-dimensional Lie superalgebras whose even part is a three-dimensional simple Lie algebra over a field of characteristic not two or three

2017/09/30 by Philippe Meyer
Mathematics · Physics and Astronomy · #Adjoint representation #Adjoint representation of a Lie algebra #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Fundamental representation #Graded Lie algebra #Killing form #Lie algebra #Lie conformal algebra #Lie superalgebra #Nonlinear Waves and Solitons #Simple Lie group #math.RA #math.RT

paper · pdf · doi:10.1080/00927872.2019.1588978

published as Communications in Algebra (2019), 47:11, 4654-4675

openalex publication_date 2019/04/11 · openalex created_date 2019/07/30 · arxiv created 2019/12/18 · arxiv updated 2019/12/19 · openalex updated_date 2026/08/05

Abstract

Let k be a field of characteristic not two or three. We classify up to isomorphism all finite-dimensional Lie superalgebras g=g0⊕g1 over k, where g0 is a three-dimensional simple Lie algebra. If Z(g) denotes the center of g, the result is the following: either g1,g1=0 or g1=(g0⊕k)⊕Z(g) or g≅ospk(1|2)⊕Z(g).

Citations

• Lie superalgebras