Graded modules for Virasoro-like algebra

2007/12/02 by Weiqiang Lin, Lin, Weiqiang, Yucai Su +1
Mathematics · Physics and Astronomy · #17B10 #17B65 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B10 #msc:17B65 #msc:17B68

paper · pdf · doi:10.48550/arxiv.0712.0144

17pages, 0 figures

arxiv created 2007/12/02 · openalex publication_date 2007/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the classification of irreducible \bf Z- and \bf Z²-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight irreducible modules. As a consequence, we also determine all the modules with nonzero center. Finally, we prove that there does not exist any nontrivial \bf Z-graded modules of intermediate series.

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