Enlacements and representation theory of completely reducible orders

1986 ◽  
pp. 272-308 ◽  
Author(s):  
Wolfgang Rump
Keyword(s):  
Representation Theory ◽  
Completely Reducible

On Extending Projectives of Finite Group-Graded Algebras

1991 ◽  
Vol 34 (2) ◽  
pp. 224-228
Author(s):  
Morton E. Harris
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Group Representation ◽  
Sufficient Conditions ◽  
Projective Cover ◽  
Graded Algebras ◽  
Finite Dimensional ◽  
Completely Reducible ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractLet G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.

scholarly journals PLAIN REPRESENTATIONS OF LIE ALGEBRAS

2001 ◽  
Vol 63 (3) ◽  
pp. 571-591 ◽  
Author(s):  
A. A. BARANOV ◽  
A. E. ZALESSKII
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
General Problem ◽  
Associative Algebras ◽  
Ground Field ◽  
Finite Dimensional ◽  
Representations Of Lie Algebras ◽  
Completely Reducible ◽  
Finite Dimensional Lie Algebras

In this paper we study representations of finite dimensional Lie algebras. In this case representations are not necessarily completely reducible. As the general problem is known to be of enormous complexity, we restrict ourselves to representations that behave particularly well on Levi subalgebras. We call such representations plain (Definition 1.1). Informally, we show that the theory of plain representations of a given Lie algebra L is equivalent to representation theory of finitely many finite dimensional associative algebras, also non-semisimple. The sense of this is to distinguish representations of Lie algebras that are of complexity comparable with that of representations of associative algebras. Non-plain representations are intrinsically much more complex than plain ones. We view our work as a step toward understanding this complexity phenomenon.We restrict ourselves also to perfect Lie algebras L, that is, such that L = [L, L]. In our main results we assume that L is perfect and [sfr ][lfr ]2-free (which means that L has no quotient isomorphic to [sfr ][lfr ]2). The ground field [ ] is always assumed to be algebraically closed and of characteristic 0.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

On the Positivity of $\mathbf{{a}}$-Linear with Random Finitely

2020 ◽  
Author(s):  
Amanda Bolton
Keyword(s):  
Representation Theory ◽  
Central Problem ◽  
Numerical Representation

Let $\rho$ be an ultra-unique, reducible topos equipped with a minimal homeomorphism. We wish to extend the results of \cite{cite:0} to trivially Cartan classes. We show that $d$ is comparable to $\mathcal{{M}}$. This leaves open the question of uniqueness. Moreover, a central problem in numerical representation theory is the description of irreducible, orthogonal, hyper-unique graphs.

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