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- W3104834899 abstract "Given an algebraically closed field $Bbbk$ of characteristic zero, a Lie superalgebra $mathfrak{g}$ over $Bbbk$ and an associative, commutative $Bbbk$-algebra $A$ with unit, a Lie superalgebra of the form $mathfrak{g} otimes_Bbbk A$ is known as a map superalgebra. Map superalgebras generalize important classes of Lie superalgebras, such as, loop superalgebras (where $A=Bbbk[t, t^{-1}]$), and current superalgebras (where $A=Bbbk[t]$). In this paper, we define Weyl functors, global and local Weyl modules for all map superalgebras where $mathfrak{g}$ is either $mathfrak{sl} (n,n)$ with $n ge 2$, or a finite-dimensional simple Lie superalgebra not of type $mathfrak{q}(n)$. 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)." @default.
- W3104834899 created "2020-11-23" @default.
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- W3104834899 date "2018-05-08" @default.
- W3104834899 modified "2023-10-16" @default.
- W3104834899 title "Weyl Modules and Weyl Functors for Lie Superalgebras" @default.
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- W3104834899 doi "https://doi.org/10.1007/s10468-018-9796-2" @default.
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