Homological topics in the representation theory of restricted Lie algebras

1996 ◽  
pp. 69-119 ◽  
Author(s):  
Jörg Feldvoss
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Restricted Lie Algebras

SCHEMES OF TORI AND THE STRUCTURE OF TAME RESTRICTED LIE ALGEBRAS

2001 ◽  
Vol 63 (3) ◽  
pp. 553-570 ◽  
Author(s):  
ROLF FARNSTEINER ◽  
DETLEF VOIGT
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Classical Case ◽  
Forthcoming Paper ◽  
Structure Theory ◽  
Group Schemes ◽  
Restricted Lie Algebra ◽  
Restricted Lie Algebras ◽  
Geometric Techniques ◽  
Support Varieties

Much of the recent progress in the representation theory of infinitesimal group schemes rests on the application of algebro-geometric techniques related to the notion of cohomological support varieties (cf. [6, 8–10]). The noncohomological characterization of these varieties via the so-called rank varieties (see [21, 22]) involves schemes of additive subgroups that are the infinitesimal counterparts of the elementary abelian groups. In this note we introduce another geometric tool by considering schemes of tori of restricted Lie algebras. Our interest in these derives from the study of infinitesimal groups of tame representation type, whose determination [12] necessitates the results to be presented in §4 and §5 as well as techniques from abstract representation theory.In contrast to the classical case of complex Lie algebras, the information on the structure of a restricted Lie algebra that can be extracted from its root systems is highly sensitive to the choice of the underlying maximal torus. Schemes of tori obviate this defect by allowing us to study algebraic families of root spaces. Accordingly, these schemes may also shed new light on various aspects of the structure theory of restricted Lie algebras. We intend to pursue these questions in a forthcoming paper [13], and focus here on first applications within representation theory.

scholarly journals Geometric representation theory of restricted Lie algebras

2001 ◽  
Vol 6 (2) ◽  
pp. 175-191 ◽  
Author(s):  
I. Mirković ◽  
D. Rumynin
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Geometric Representation ◽  
Geometric Representation Theory ◽  
Restricted Lie Algebras

scholarly journals Filtrations for periodic modules over restricted Lie algebras

1992 ◽  
Vol 3 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Daniel K. Nakano
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras

INTRODUCTION TO LIE ALGEBRAS AND REPRESENTATION THEORY

1974 ◽  
Vol 6 (2) ◽  
pp. 237-238
Author(s):  
W. Ledermann
Keyword(s):  
Representation Theory ◽  
Lie Algebras

scholarly journals Restricted Lie algebras of characteristic $p$

1941 ◽  
Vol 50 (1) ◽  
pp. 15-15
Author(s):  
N. Jacobson
Keyword(s):  
Lie Algebras ◽  
Characteristic P ◽  
Restricted Lie Algebras

Auslander-Reiten theory for restricted Lie algebras

1998 ◽  
Author(s):  
R. Farnsteiner
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras

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

Finite group schemes of p-rank ≤ 1

2017 ◽  
Vol 166 (2) ◽  
pp. 297-323
Author(s):  
HAO CHANG ◽  
ROLF FARNSTEINER
Keyword(s):  
Finite Group ◽  
Lie Algebras ◽  
Group Scheme ◽  
Closed Field ◽  
Difficult Case ◽  
Modular Representation Theory ◽  
Group Schemes ◽  
Restricted Lie Algebras ◽  
A Finite Group ◽  
Finite Group Schemes

AbstractLet be a finite group scheme over an algebraically closed field k of characteristic char(k) = p ≥ 3. In generalisation of the familiar notion from the modular representation theory of finite groups, we define the p-rank rkp() of and determine the structure of those group schemes of p-rank 1, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height 1, which correspond to restricted Lie algebras. Our results show that group schemes of p-rank ≤ 1 are closely related to those being of finite or domestic representation type.

scholarly journals The cohomology of restricted Lie algebras and of Hopf algebras

1965 ◽  
Vol 71 (2) ◽  
pp. 372-378 ◽  
Author(s):  
J. Peter May
Keyword(s):  
Lie Algebras ◽  
Hopf Algebras ◽  
Restricted Lie Algebras
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