Induced 3-Lie algebras, superalgebras and induced representations; pp. 116–133

Proceedings of the Estonian Academy of Sciences

article

Viktor Abramov¹  Priit Lätt¹ 

[1] Institute of Mathematics and Statistics, University of Tartu

关键词: 3-Lie algebra;    3-Lie superalgebra;    Filippov–Jacobi identity;    commutative algebras with involution and derivation;    representations of 3-Lie algebras and superalgebras;   

DOI  :  10.3176/proc.2020.2.05

学科分类：内科医学

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

We construct 3-Lie superalgebras on a commutative superalgebra by means of involution and even degree derivation. We construct a representation of induced 3-Lie algebras and superalgebras by means of a representation of initial (binary) Lie algebra, trace and supertrace. We show that the induced representation of 3-Lie algebra, that we constructed, is a representation by traceless matrices, that is, lies in the Lie algebra sl(V ), where V is a representation space. In the case of 2-dimensional representation we find conditions under which the induced representation of induced 3-Lie algebra is irreducible. We give the example of irreducible representation of induced 3-Lie algebra of 2nd order complex matrices.

【 授权许可】

CC BY