Cohomology of graded lie algebras of cartan type of Characteristic p

1987 ◽  
Vol 57 (1) ◽  
pp. 139-156 ◽  
Author(s):  
Chiu Sen ◽  
Shen Guangyu
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras ◽  
Characteristic P ◽  
Cartan Type

ON CARTAN INVARIANTS FOR GRADED LIE ALGEBRAS OF CARTAN TYPE

2013 ◽  
Vol 13 (03) ◽  
pp. 1350101
Author(s):  
BIN SHU ◽  
YU-FENG YAO
Keyword(s):  
Lie Algebra ◽  
Closed Field ◽  
Graded Lie Algebras ◽  
Characteristic P ◽  
Cartan Type ◽  
Restricted Lie Algebra ◽  
Projective Representations ◽  
Cartan Invariants ◽  
The One ◽  
Special Case

Let L = X(m; n), X ∈ {W, S, H, K}, be a graded simple Lie algebra of Cartan type over an algebraically closed field of characteristic p > 3. Then L is a so-called generalized restricted Lie algebra. Let [Formula: see text] be the primitive p-envelope of L, and G = X(m; 1), a subalgebra of [Formula: see text]. In this paper, a close connection between Cartan invariants for [Formula: see text] and U(G, χ) is established, where χ ∈ L* is extended to be a linear function on [Formula: see text] trivially, and 1 ≤ ht (χ) < p-2+δXW. This reduces the study of projective representations of the generalized restricted Lie algebra L to the one of the corresponding restricted Lie algebra G. As a special case, we recover some results in [Shu and Jiang, On Cartan invariants and blocks of Zassenhaus algebras, Comm. Algebra33(10) (2005) 3619–3630].

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