
Journal of Lie Theory 32 (2022), No. 1, 267279 Copyright Heldermann Verlag 2022 Partial Classification of Irreducible Modules for LoopWitt Algebras Priyanshu Chakraborty School of Mathematics, HarishChandra Research Institute, PrayagrajAllahabad, Uttar Pradesh, India priyanshuchakraborty@hri.res.in S. Eswara Rao School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India senapati@math.tifr.res.in [Abstractpdf] 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 $(A\rtimes Der\,A)\otimes B$. Keywords: Witt algebra, Virasoro algebra, current algebra. MSC: 17B65,17B68,17B67. [ Fulltextpdf (131 KB)] for subscribers only. 