Weyl Modules and Weyl Functors for Lie Superalgebras

Author(s)

Bagci, Irfan ^[1] ; Calixto, Lucas ^[2] ; Macedo, Tiago ^[3]

Affiliation

^[1] Univ North Georgia, Dept Math, Oakwood, GA 30566 - USA

^[2] Univ Fed Minas Gerais, Dept Math, BR-30123970 Belo Horizonte, MG - Brazil

^[3] Univ Fed Sao Paulo, Dept Sci & Technol, BR-12247014 Sao Jose Dos Campos, SP - Brazil

• Document type: Journal article
• Source: ALGEBRAS AND REPRESENTATION THEORY; v. 22, n. 3, p. 723-756, JUN 2019.
• Web of Science Citations: 0

Abstract

Given an algebraically closed field ? of characteristic zero, a Lie superalgebra ? over ? and an associative, commutative ?-algebra A with unit, a Lie superalgebra of the form ? circle times(?)A is known as a map superalgebra. Map superalgebras generalize important classes of Lie superalgebras, such as, loop superalgebras (where A = ?{[}t(+/- 1)]), and current superalgebras (where A = ?{[}t]). In this paper, we define Weyl functors, global and local Weyl modules for all map superalgebras where ? is either ??(n, n) with n 2, or a finite-dimensional simple Lie superalgebra not of type ?(n). Under certain conditions on the triangular decomposition of these Lie superalgebras we prove that global and local Weyl modules satisfy certain universal and tensor product decomposition properties. We also give necessary and sufficient conditions for local (resp. global) Weyl modules to be finite dimensional (resp. finitely generated). (AU)

• FAPESP's process: 13/08430-4 - Representations of map superalgebras
• Grantee: Lucas Henrique Calixto
• Support Opportunities: Scholarships in Brazil - Doctorate