Communications in Algebra· 2026Q2
The solenoidal Heisenberg-Virasoro algebra and its simple weight modules
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- Q2SCImago
- 2026year
Short summary
Researchers constructed a higher rank Heisenberg-Virasoro algebra, HVir(n)μ, and identified two types of simple weight modules: intermediate series and generalized highest weight (GHW) modules.
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Key points
- Introduced HVir(n)μ, a higher rank Heisenberg-Virasoro algebra, as a universal central extension.
- Identified two classes of Harish-Chandra modules for HVir(n)μ: intermediate series and GHW modules.
- Developed a triangular decomposition of HVir(n)μ using lexicographic order.
- Constructed irreducible weight modules with infinite-dimensional weight spaces.
AI-generated from the title and abstract; the full text is not read.
Abstract
The aim of this paper is to study the universal central extension of the semi-direct Lie algebra WA(n)μ:=W(n)μ⋉An where An:=C[ti±1, 1≤i≤n] is the algebra of Laurent polynomials in n variables and W(n)μ:=Andμ is the solenoidal Lie algebra introduced by Y.Billig and V.Futorny in [Citation6]. Here μ=(μ1,…,μn)∈Cn is a generic vector and dμ=∑i=1nμiti∂∂ti. The obtained algebra is a higher rank Heisenberg-Virasoro algebra denoted by HVir(n)μ (see [Citation15,Citation16]). Moreover, we study Harish-Chandra HVir(n)μ-modules following [Citation16]. We obtain two kinds of such modules, intermediate series modules and generalized highest weight modules(GHW modules). Furthermore, we use the lexicographic order on Zn to give a triangular decomposition of HVir(n)μ which allows us to construct irreducible weight modules which have infinite dimensional weight spaces.
The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics