Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations

Symmetry Integrability and Geometry-Methods and Applications

article

Sofiane Bouarroudj¹  Pavel Grozman¹  Alexei Lebedev¹  Dimitry Leites²  Irina Shchepochkina⁴ 

[1] New York University Abu Dhabi, Division of Science and Mathematics, United Arab Emirates;Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis;St. Petersburg State University;Independent University of Moscow

关键词: modular vectorial Lie algebra;    modular vectorial Lie superalgebra 2020 Mathematics Subject Classification 17B50;    17B20;    70F25;   

DOI  :  10.3842/SIGMA.2020.089

来源: National Academy of Science of Ukraine

【 摘 要 】

We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformations. For all 15 Weisfeiler gradings of the 5 exceptional families, and one Weisfeiler grading for each of 2 serial simple complex Lie superalgebras (with 2 exceptional subseries), we describe their characteristic-2 analogs - new simple Lie algebras. Descriptions of several of these analogs, and of their desuperizations, are far from obvious. One of the exceptional simple vectorial Lie algebras is a previously unknown deform (the result of a deformation) of the characteristic-2 version of the Lie algebra of divergence-free vector fields; this is a new simple Lie algebra with no analogs in characteristics distinct from 2. In characteristic 2, every simple Lie superalgebra can be obtained from a simple Lie algebra by one of the two methods described in arXiv:1407.1695. Most of the simple Lie superalgebras thus obtained from simple Lie algebras we describe here are new.

【 授权许可】

Unknown