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Simple modules over the Lie algebras of divergence zero vector fields on a torus
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China.
Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China.
Hebei Normal Teachers Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Hebei, Peoples R China;Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada.
2019 (English)In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 31, no 3, p. 727-741Article in journal (Refereed) Published
Abstract [en]

Let n >= 2 be an integer, S-n the Lie algebra of divergence zero vector fields on an n-dimensional torus, and K-n the Weyl algebra over the Laurent polynomial algebra A(n) = C[x(1)(+/- 1), x(2)(+/- 1), . . . , x(n)(+/- 1)]. For any sln-module V and any module P over K-n, we define an S-n-module structure on the tensor product P circle times V. In this paper, necessary and sufficient conditions for the S-n-modules P circle times V to be simple are given, and an isomorphism criterion for nonminuscule S-n-modules is provided. More precisely, all nonminuscule S-n-modules are simple, and pairwise nonisomorphic. For minuscule S-n-modules, minimal and maximal submodules are concretely determined.

Place, publisher, year, edition, pages
2019. Vol. 31, no 3, p. 727-741
Keywords [en]
Lie algebra of divergence zero vector fields, Weyl algebra, irreducible module, (non)minuscule module, density theorem
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-383509DOI: 10.1515/forum-2018-0096ISI: 000465554800011OAI: oai:DiVA.org:uu-383509DiVA, id: diva2:1316237
Available from: 2019-05-16 Created: 2019-05-16 Last updated: 2019-05-16Bibliographically approved

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Dubsky, Brendan Frisk

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