Equivariant Map Queer Lie Superalgebras

Author(s)

Calixto, Lucas ^[1] ; Moura, Adriano ^[1] ; Savage, Alistair ^[2]

Affiliation

^[1] UNICAMP IMECC, BR-13083859 Campinas, SP - Brazil

^[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON - Canada

• Document type: Journal article
• Source: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES; v. 68, n. 2, p. 258-279, APR 2016.
• Web of Science Citations: 3

Abstract

An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) X to a queer Lie superalgebra q that are equivariant with respect to the action of a finite group Gamma acting on X and q. In this paper, we classify all irreducible finite dimensional representations of the equivariant map queer Lie superalgebras under the assumption that Gamma is abelian and acts freely on X. We show that such representations are parameterized by a certain set of Gamma-equivariant finitely supported maps from X to the set of isomorphism classes of irreducible finite-dimensional representations of q. In the special case where X is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra. (AU)

• FAPESP's process: 13/08430-4 - Representations of map superalgebras
• Grantee: Lucas Henrique Calixto
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants