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

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Bin Shu
Keyword(s):  
Lie Algebras ◽  
Generic Property ◽  
Conjugacy Classes ◽  
Type I ◽  
Cartan Type ◽  
Restricted Lie Algebras

Borel subalgebras of restricted Cartan-Type Lie algebras

2021 ◽  
pp. 2250210
Author(s):  
Ke Ou ◽  
Bin Shu
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Open Problem ◽  
Conjugacy Classes ◽  
Classical Type ◽  
Geometric Representation ◽  
Cartan Type ◽  
Geometric Representation Theory ◽  
Geometric Setting

It is still an open problem to determine the conjugacy classes of Borel subalgebras of non-classical type Lie algebras. In this paper, we prove that there are at least 2 conjugacy classes of Borel subalgebras as well as maximal triangulable subalgebras of restricted Cartan type Lie algebras of type W, S and H. We are particularly interested in maximal triangulable subalgebras of [Formula: see text] under some conditions which is called [Formula: see text]-subalgebras (Definition 3.1). We classify the conjugacy classes of [Formula: see text]-subalgebras for [Formula: see text] and determine their representatives. This paper and its sequel [Z. Lin, K. Ou and B. Shu, Geometric Setting of Jacobson–Witt Algebras, preprint] attempt to establish both algebraic and geometric setting for geometric representation theory of [Formula: see text]

Endotrivial modules for nilpotent restricted Lie algebras

2020 ◽  
Vol 114 (5) ◽  
pp. 503-513
Author(s):  
David J. Benson ◽  
Jon F. Carlson
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras
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