Classification of Z²-graded modules of the intermediate series over a Lie algebra of Block type

2006/11/30 by Xiaoqing Yue, Yue, Xiaoqing, Yucai Su +1
Mathematics · #17B10 #17B65 #17B68 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B10 #msc:17B65 #msc:17B68

paper · pdf · doi:10.48550/arxiv.math/0611942

LaTex, 16 pages

openalex publication_date 2006/11/30 · arxiv created 2007/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be the Lie algebra of Block type over a field F of characteristic zero, defined with basis L_i,j | i,j∈ Z and relations [L_i,j,L_k,l]=((j+1)k-(l+1)i)L_i+k,j+l. Then L is Z²-graded. In this paper, Z²-graded L-modules of the intermediate series are classified.

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