2024/03/06 by Boujemaâ Agrebaoui, Agrebaoui, Boujemaa, Walid Mhiri +1
Mathematics · Physics and Astronomy · #17B10 #17B20 #17B68 #17B86 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2403.03753
openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let An=ℂ[ti±1,~1≤ i≤ n] be the algebra of Laurent polynomials in n-variables. Let μ=(μ1,…,μn) be a generic vector in ℂn and Γμ=\μ⋅α,α∈ ℤn\ where μ⋅α=∑i=1nμiαi for α=(α1,…,αn)∈ ℤn. Denote by dμ the vector field: dμ=∑i=1nμiti(d)/(dti). In \citeBiFu, Y. Billig and V. Futorny introduce the solenoidal Lie algebra W(n)μ:=Andμ, where the Lie structure is given by the commutators of vector fields. In the first part of this paper, we study the universal central extension of W(n)μ. We obtain a rank n Virasoro algebra called the solenoidal Virasoro algebra Vir(n)μ. In the second part, we recall in the case of Vir(n)μ, the well know Harich-Chandra modules for generalized Virasoro algebra studied in \citeSu,Su1,LuZhao. In the third part, we construct irreducible highest and lowest Vir(n)μ-modules using triangular decomposition given by lexicographic order on ℤn. We prove that these modules are weight modules which have infinite dimensional weight spaces.