Transposed Poisson 3-Lie superalgebras

Abstract

Käesolev magistritöö on pühendatud Lie algebrate ja Poissoni algebrate mõiste üldistustele. Töös uuritakse transponeeritud Poissoni superalgebraid ja nende seost 3-Lie superalgebratega. Sisse tuuakse ja uuritakse transponeeritud 3-Lie Poissoni superalgebra mõistet. Esitatakse meetod transponeeritud 3-Lie Poissoni superalgebrate konstrueerimiseks transponeeritud Poissoni superalgebrate paarisderivatsioonide abil. Selle meetodi abil konstrueeritakse lai klass transponeeritud 3-Lie Poissoni superalgebraid kommutatiivse superalgebra ning selle kahe kommuteeruva paarisderivatsiooni korral.

This master thesis is devoted to generalizations of the concepts of Lie algebras and Poisson algebras. The thesis studies transposed Poisson superalgebras and their connection with 3-Lie superalgebras. The notion of a transposed 3-Lie Poisson superalgebra is introduced and investigated. The thesis proposes a method for constructing transposed 3-Lie Poisson superalgebras by means of even derivations of transposed Poisson superalgebras. Using this method, a wide class of transposed 3-Lie Poisson superalgebras is constructed for the case of a commutative superalgebra and its two commuting even derivations.