A finite number of defining relations and a UCE theorem of the elliptic Lie algebras and superalgebras with rank ≥ 2

2004/08/26 by Hiroyuki Yamane, Yamane, Hiroyuki
Mathematics · #17B65 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B65

paper · pdf · doi:10.48550/arxiv.math/0408362

30 pages

arxiv created 2004/08/26 · openalex publication_date 2004/08/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a finite number of defining relations satisfied by a finite number of generators for the elliptic Lie algebras and superalgebras \frak g_R with rank ≥ 2. Here the R's denote the reduced and non-reduced elliptic root systems with rank ≥ 2. We also show that if \cal L is an extended affine Lie algebra (EALA) whose non-isotropic roots form the R, then there exists a natural homomorphism \cal F:\frak g_R →\cal L, which also give a universal central extension (UCE) surjective map from [\frak g_R,\frak g_R] to the core of \cal L. (More precisely, we take a \frak g_R instead of the \frak g_R.)

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