Author:
GRANTCHAROV DIMITAR,PENKOV IVAN
Abstract
Abstract
We classify the simple bounded weight modules of the Lie algebras $$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right) $$
sl
∞
,
o
∞
and $$ \mathfrak{sp}\left(\infty \right) $$
sp
∞
, and compute their annihilators in $$ U\left(\mathfrak{sl}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{o}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{sp}\left(\infty \right)\right) $$
U
sl
∞
,
U
o
∞
,
U
sp
∞
, respectively.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Reference22 articles.
1. A. Baranov, Complex finitary simple Lie algebras, Arch. Math. 71 (1998), 1–6.
2. G. Benkart, D. Britten, F. Lemire, Modules with bounded weight multiplicities for simple Lie algebras, Math. Z. 225 (1997), 333–353.
3. D. Britten, F. Lemire, A classiffication of simple Lie modules having a 1-dimensional weight space, Trans. Amer. Math. Soc. 299 (1987), 683–697.
4. K. Coulembier, I. Penkov, On an infinite limit of BGG categories $$ \mathcal{O} $$, to appear in Moscow Math. J., arXiv:1802.06343 (2018).
5. E. Dan-Cohen, I. Penkov, V. Serganova, A Koszul category of representations of finitary Lie algebras, Adv. Math. 289 (2016), 250–278.
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献