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- Title
Varieties of Borel subalgebras for the Jacobson–Witt Lie algebras.
- Authors
Ou, Ke; Shu, Bin
- Abstract
Let W (n) be the Jacobson–Witt algebra over algebraic closed field 핂 with characteristic p > 2 . In [K. Ou and B. Shu, Borel subalgebras of restricted Cartan-type Lie algebras, J. Algebra Appl. 21 2022, 11, Paper No. 2250210], we introduced the so-called B-subalgebra of W (n) , which serves as an analog of the Borel subalgebra of classical Lie algebras. As a sequel, we describe the structure of the variety ℬ consisting of all B-subalgebras of W (n) in this paper. This variety presents an analog of the flag variety for classical Lie algebras. It is shown that ℬ is related to the variety of all full flags in 핂 n + 1 . Additionally, we provide a detailed description of the varieties for W (1) as an illustrative example. With the above setting-up, one may establish the Springer theory and geometric representations for the Jacobson–Witt algebras.
- Subjects
LIE algebras; REPRESENTATIONS of algebras; REPRESENTATION theory; ALGEBRAIC fields; ALGEBRA
- Publication
Forum Mathematicum, 2023, Vol 35, Issue 6, p1583
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2022-0336