1School of Mathematics, Harish-Chandra Research Institute, Prayagraj-Allahabad, Uttar Pradesh, India 2School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India
Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 267-279
Consider the Lie algebra of the group of diffeomorphisms of a $n$-dimensional torus which is also known as the derivation algebra of the Laurent polynomial algebra $A$ over $n$ commuting variables, denoted by $Der\,A$. In this paper we consider the Lie algebra $(A\rtimes Der\,A)\otimes B$ for some commutative associative unital algebra $B$ over $\mathbb C$ and classify all irreducible modules for $(A\rtimes Der\,A) \otimes B$ with finite dimensional weight spaces under some natural conditions. In particularly, we show that Larsson's constructed modules of tensor fields exhaust all such irreducible modules for $(A\rtimes Der\,A)\otimes B$.
1
School of Mathematics, Harish-Chandra Research Institute, Prayagraj-Allahabad, Uttar Pradesh, India
2
School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India
Priyanshu Chakraborty; S. Eswara Rao. Partial Classification of Irreducible Modules for Loop-Witt Algebras. Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 267-279. http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a13/
@article{JOLT_2022_32_1_a13,
author = {Priyanshu Chakraborty and S. Eswara Rao},
title = {Partial {Classification} of {Irreducible} {Modules} for {Loop-Witt} {Algebras}},
journal = {Journal of Lie Theory},
pages = {267--279},
year = {2022},
volume = {32},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a13/}
}
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AU - S. Eswara Rao
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