Irreducible modules for equivariant map superalgebras and their extensions

JOURNAL OF ALGEBRA

卷:517

Article

Calixto, Lucas¹  Macedo, Tiago^2,3 

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

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

[3] Univ Fed Sao Paulo, Dept Sci & Technol, BR-12247014 Sao Paulo, Brazil

关键词: Lie superalgebra;    Representation theory;    Homological methods;   

DOI  :  10.1016/j.jalgebra.2018.10.001

来源: Elsevier

【 摘 要 】

Let Gamma be a group acting on a scheme X and on a Lie superalgebra g, both defined over an algebraically closed field of characteristic zero k. The corresponding equivariant map superalgebra M(g, X)(Gamma) is the Lie superalgebra of Gamma-equivariant regular maps from X to g. In this paper we complete the classification of finite-dimensional irreducible M(g, X)(Gamma)-modules when g is a finite-dimensional simple Lie superalgebra, X is of finite type and Gamma is a finite abelian group acting freely on the rational points of X, by classifying these M(g, X)(Gamma)-modules in the case where g is a periplectic Lie superalgebra. We also describe extensions between irreducible modules in terms of homomorphisms and extensions between modules for certain finite-dimensional Lie superalgebras. As an application, one obtains the block decomposition of the category of finite-dimensional M(g, X)(Gamma)-modules in terms of blocks and spectral characters of finite-dimensional Lie superalgebras. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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