2025/06/17 by Jin Cheng, Cheng, Jin, Dongfang Gao +3 · 1 citation
Mathematics · #17B10 #17B65 #17B66 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2506.14893
openalex publication_date 2025/06/17 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
In this paper, we investigate the irreducible tensor product modules over the planar Galilean conformal algebra G named by Aizawa, which is the infinite-dimensional Galilean conformal algebra introduced by Bagchi-Gopakumar in (2+1) dimensional space-time. We give the necessary and sufficient conditions for the tensor product modules of any two of U(\mathfrakh)-free modules of rank one over G to be irreducible, where \mathfrakh is the Cartan subalgebra of G.Furthermore, the isomorphism classes of these irreducible tensor product modules are determined. As an application, we obtain the necessary conditions for the tensor product modules of any two of U(ℂ L0)-free modules of rank one over Witt algebra and Heisenberg-Virasoro algebra to be irreducible.