Irreducible representations of simple linearly compact n-Lie superalgebras of type W

BOYALLIAN CARINA; MEINARDI VANESA

College Station

Seminario; Algebra and Combinatorics Seminar; 2015

Texas A&M University

In the past few years there has been some interest in n-Lie algebras in the physics community related to M-branes in string theory. In 2010, Cantarini and Kac classified all simple linearly compact n-Lie superalgebras with n > 2 over a field F of characteristic 0. The list consists of four examples, one of them being the n-Lie algebra denoted by W^n, which is the linearly compact vector space of formal power series F[[x_1,ldots,x_{n-1}]] endowed with an n-ary bracket. In a joint work with C. Boyallian, we classified all irreducible representations of the n-Lie superalgebras of type W.In this talk, we will introduce basic definitions and some general results over representations of the simple linearly compact n-Lie superalgebras. We will also present the classification of all irreducible representations of the n-Lie algebra W^n for the cases n=3 and n=4.