Highest weight representations of a Lie algebra of Block type
| dc.creator | Wu, Yuezhu | |
| dc.creator | Su, Yucai | |
| dc.date | 2005-11-30 | |
| dc.date.accessioned | 2026-07-07T06:51:55Z | |
| dc.date.available | 2026-07-07T06:51:55Z | |
| dc.description | For 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.description | LaTeX, 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511733 | |
| dc.identifier | http://arxiv.org/abs/math/0511733 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105148 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10; 17B65; 17B68 | |
| dc.title | Highest weight representations of a Lie algebra of Block type | |
| dc.type | text |