Irreducible representations of nongraded Witt type Lie algebras
Irreducible representations of nongraded Witt type Lie algebras
复制标题
DOI：
10.1016/j.jalgebra.2005.10.002
复制
发表时间：
2006-04
影响因子：
0.9
通讯作者：
Yufeng Zhao
中科院分区：
文献类型：
--
作者：
Yufeng Zhao
Xu从可积系统中对应于某些哈密顿对的二次共形代数的分类出发，给出了与某些交换结合代数上有限的局部有限导集相关的7类非分级无限维简单李代数的显式构造。本文在一般线性李代数有限维不可约模的基础上，构造了非分级Witt型李代数的不可约广义权模族。我们的结果是非分级推广的Rao的工作的推导李代数的不可约表示的劳伦多项式的代数在几个变量。
From his classification of quadratic conformal algebras corresponding to certain Hamiltonian pairs in integrable systems, Xu gave an explicit construction of seven types of nongraded infinite-dimensional simple Lie algebra related to a finite set of locally-finite derivations on certain commutative associative algebras. In this paper, we construct a family of irreducible generalized weight modules for the nongraded Witt type Lie algebras based on finite-dimensional irreducible modules of general linear Lie algebras. Our results are nongraded generalizations of Rao's work on irreducible representations of the derivation Lie algebra of the algebra of Laurent polynomials in several variables.