A Class of Polynomial Modules over Map Lie Algebras

被引：0
|
作者：
Chen, Hongjia [1 ]
Dai, Han [1 ]
Liu, Xingpeng [1 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei, Anhui, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2024年
基金：
中国国家自然科学基金;
关键词：
Map Lie algebras; U(h)-free modules; Simple Lie algebras; WEIGHT MODULES; REPRESENTATIONS;
D O I：
10.1007/s40304-023-00356-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For any finitely generated unital commutative associative algebra R over C and any complex finite-dimensional simple Lie algebra g with a fixed Cartan subalgebra h, we classify all g circle times R-modules on U (h) such that h as a subalgebra of g circle times R, acts on U (h) by the multiplication. We construct these modules explicitly and study their module structures.
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页数：21
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