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- Title
The BGG Category for Generalized Reductive Lie Algebras.
- Authors
Ren, Ye
- Abstract
A Lie algebra g is considered generalized reductive if it is a direct sum of a semisimple Lie algebra and a commutative radical. This paper extends the BGG category O over complex semisimple Lie algebras to the category O ′ over complex generalized reductive Lie algebras. Then, we preliminarily research the highest weight modules and the projective modules in this new category O ′ , and generalize some conclusions for the classical case. Also, we investigate the associated varieties with respect to the irreducible modules in O ′ and obtain a result that extends Joseph's result on the associated varieties for reductive Lie algebras. Finally, we study the center of the universal enveloping algebra U(g ) and independently provide a new proof of a theorem by Ou–Shu–Yao for the center in the case of enhanced reductive Lie algebras.
- Subjects
LIE algebras; COMMUTATIVE algebra; UNIVERSAL algebra
- Publication
Frontiers of Mathematics, 2024, Vol 19, Issue 1, p127
- ISSN
2731-8648
- Publication type
Article
- DOI
10.1007/s11464-021-0352-8