Journal of Lie Theory

no. 1
Partial Classification of Irreducible Modules for Loop-Witt Algebras
Journal of Lie Theory, Volume 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 $(A\rtimes Der\,A)\otimes B$.
DOI: 10.5802/jolt.1230
Classification: 17B65,17B68,17B67
Keywords: Witt algebra, Virasoro algebra, current algebra 
@article{JOLT_2022_32_1_a13,
     author = {P. 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},
     doi = {10.5802/jolt.1230},
     zbl = {1486.17037},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1230/}
}
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P. Chakraborty; S. Eswara Rao. Partial Classification of Irreducible Modules for Loop-Witt Algebras. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 267-279. doi: 10.5802/jolt.1230

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