Classification of Quasifinite Modules over the Lie Algebras of Weyl Type
| dc.creator | Su, Yucai | |
| dc.date | 2003-04-03 | |
| dc.date.accessioned | 2026-07-07T04:56:34Z | |
| dc.date.available | 2026-07-07T04:56:34Z | |
| dc.description | For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all differential operators $u D_1^{m_1}... D_n^{m_n}$ for $u\in F[G]$ (the group algebra), and $m_1,...,m_n \ge 0$, where $D_1, ...,D_n$ are degree operators. In this paper, it is proved that an irreducible quasifinite $W(\Z,1)$-module is either a highest or lowest weight module or else a module of the intermediate series; furthermore, a classification of uniformly bounded $W(\Z,1)$-modules is completely given. It is also proved that an irreducible quasifinite $W(G,n)$-module is a module of the intermediate series and a complete classification of quasifinite $W(G,n)$-modules is also given, if $G$ is not isomorphic to $\Z$. | |
| dc.description | 11 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0304033 | |
| dc.identifier | http://arxiv.org/abs/math/0304033 | |
| dc.identifier | Adv. Math., 174 (2003), 57-68 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66968 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B65 | |
| dc.title | Classification of Quasifinite Modules over the Lie Algebras of Weyl Type | |
| dc.type | text |