2019 / September Volume 14 No.3
Generic Property and Conjugacy Classes of Homogeneous Borel Subalgebras of Restricted Lie Algebras of Cartan Type (I): Type W
| Published Date |
2019 / September
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|---|---|
| Title | Generic Property and Conjugacy Classes of Homogeneous Borel Subalgebras of Restricted Lie Algebras of Cartan Type (I): Type W |
| Author | |
| Keyword | |
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| Pagination | 295-329 |
| Abstract | Let $(\mathfrak g,[p])$ be a finite-dimensional restricted Lie algebra over an algebraically closed field $\mathbb K$
of characteristic $p>0$, and $G$ be the adjoint group of $\mathfrak g$. We say that $\mathfrak g$ satisfies the {\sl generic property} if $\mathfrak g$ admits generic tori introduced in [2]. In this paper, we first prove a generalized conjugacy theorem for Cartan subalgebras by means of the generic property. We then classify
the $G$-conjugacy classes of homogeneous Borel subalgebras of the restricted simple
Lie algebras $\mathfrak g=W(n)$ when $p>3$, and determine
representatives of these classes. Here $W(n)$ is the so-called Jacobson-Witt algebra, by definition the derivation algebra of the truncated polynomial ring $\mathbb K[T_1,\cdots,T_n]/(T_1^p,\cdots,T_n^p)$. We also describe the closed
connected solvable subgroups of $G$ associated with those representative Borel subalgebras.
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| DOI | |
| AMS Subject Classification |
17B50, 17B05, 17B20
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| Received |
2018-04-04
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| Accepted |
2018-09-13
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