1. Simple 픰픩d+1-modules from Witt algebra modules.
- Author
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Guo, Xiangqian, Liu, Xuewen, and Zhang, Fenghua
- Subjects
- *
VECTOR spaces , *LINEAR algebra , *ALGEBRA - Abstract
Let d ≥ 1 be an integer and let 풲 d be the Witt algebra. For any admissible 풲 d -module P and any 픤 픩 d -module V, one can form a 풲 d -module ℱ (P , V) , which as a vector space is P ⊗ V . Since 풲 d has a natural subalgebra isomorphic to 픰 픩 d + 1 , we can view ℱ (P , V) as an 픰 픩 d + 1 -module. Taking P = Ω (흀) , the rank-1 U (픥) -free 풲 d -module, and V = V (퐚 , b) , the simple cuspidal module over 픤 픩 d , we get the special 픰 픩 d + 1 -modules ℱ (흀 ; 퐚 , b) = ℱ (Ω (흀) , V (퐚 , b)) which are U (픥) -free modules of infinite rank. We determine the necessary and sufficient condition for the 픰 픩 d + 1 -module ℱ (흀 ; 퐚 , b) to be simple, and for the non-simple case we construct their proper submodules explicitly. At last, using the above results, we deduce an explicit simplicity criterion for the generalized Verma modules induced from V (퐚 , b) and obtain a family of simple affine modules from ℱ (흀 ; 퐚 , b) , which can be viewed as the non-weight version of loop modules. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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