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Generic Property and Conjugacy Classes of Homogeneous Borel Subalgebras of Restricted Lie Algebras of Cartan Type (I): Type W

2019
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Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES
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Let (g, [p] ) be a finite-dimensional restricted Lie algebra over an algebraically closed field K of characteristic p > 0, and G be the adjoint group of g. We say that g satisfies the generic property if 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 g = W (n) when p > 3,

doi:10.21915/bimas.2019302
fatcat:swn5yw3gyvfo5a4k2pjtaf5s5u