Highest weight representations of a Lie algebra of Block type

dc.creatorWu, Yuezhu
dc.creatorSu, Yucai
dc.date2005-11-30
dc.date.accessioned2026-07-07T06:51:55Z
dc.date.available2026-07-07T06:51:55Z
dc.descriptionFor a field $F$ of characteristic zero and an additive subgroup $G$ of $F$, a Lie algebra $B(G)$ of lock type is defined with basis $\{L_{a,i},c|a \in G, i>-2\}$ and relations $[L_{a,i},L_{b,j}]=((i+1)b-(j+1)a)L_{a+b,i+j}+a\d_{a,-b}\d_{i+j,-2}c, [c,L_{a,i}]=0.$ Given a total order $\succ$ on $G$ compatible with its group structure, and any $Λ\in B(G)_0^*$, a Verma $B(G)$-module $M(Λ,\succ)$ is defined, and the irreducibility of $M(Λ,\succ)$ is completely determined. Furthermore, it is proved that an irreducible highest weight $B(Z)$-module is quasifinite if and only if it is a proper quotient of a Verma module.
dc.descriptionLaTeX, 13 pages
dc.identifierhttps://arxiv.org/abs/math/0511733
dc.identifierhttp://arxiv.org/abs/math/0511733
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105148
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B10; 17B65; 17B68
dc.titleHighest weight representations of a Lie algebra of Block type
dc.typetext

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