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

Bin Shu
2019 Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES  
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,
more » ... 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 K[T1, · · · , Tn]/(T p 1 , · · · , T p n ). We also describe the closed connected solvable subgroups of G associated with those representative Borel subalgebras.
doi:10.21915/bimas.2019302 fatcat:swn5yw3gyvfo5a4k2pjtaf5s5u