Typical Blocks of Lie Superalgebras in Prime Characteristic

@article{Zhao2009TypicalBO,
  title={Typical Blocks of Lie Superalgebras in Prime Characteristic},
  author={Lei Zhao},
  journal={Communications in Algebra},
  year={2009},
  volume={39},
  pages={534 - 547}
}
  • Lei Zhao
  • Published 12 May 2009
  • Mathematics
  • Communications in Algebra
For a type I basic classical Lie superalgebra , we establish an equivalence between typical blocks of categories of U χ(𝔤)-modules and -modules. We then deduce various consequences from the equivalence. 
2 Citations
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References

SHOWING 1-10 OF 27 REFERENCES
Representations of Lie superalgebras in prime characteristic I
We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-WeisfeilerExpand
ON REPRESENTATIONS OF CLASSICAL SEMISIMPLE LIE ALGEBRAS OF CHARACTERISTIC p
In this paper theorems are proved about the dimension and the structure of irreducible representations of semisimple Lie algebras with nondegenerate Killing form over a field of prime characteristic.
On simple modules for the restricted Lie superalgebra $gl(m|n)$
In this paper, we study the simple modules for the restricted Lie superalgebra $gl(m|n)$. A condition for the simplicity of the induced modules is given, and an analogue of Kac-Weisfeiler theorem isExpand
Representations of Lie superalgebras in prime characteristic II: The queer series
The modular representation theory of the queer Lie superalgebra q(n) over characteristic p>2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimpleExpand
Strongly typical representations of the basic classical Lie superalgebras
1.1. In [PS1], I. Penkov and V. Serganova show that the category of representations of a basic classical Lie superalgebra g of type I with a fixed typical central character is equivalent to theExpand
Representations of Lie algebras in prime characteristic
The aim of these lectures is to give a survey on the representation theory of Lie algebras of reductive groups in prime characteristic. This theory is quite different from the corresponding theory inExpand
Modular representation theory of Lie algebras
On etudie les representations non necessairement restreintes de l'algebre universelle enveloppante U(#7B-G) pour une algebre de Lie restreinte #7B-G
Representations of classical Lie superalgebras of type I
Abstract An explicit description of a generic irreducible module (possibly infinite dimensional and not necessarily diagonalizable over some Cartan subsuperalgebra) over a finite dimensionalExpand
Generic representations of classical Lie superalgebras and their localization
We complete the study of arbitrary generic irreducible modules over a classical complex Lie superalgebraG initiated in [14] (whereG was assumed to be of type I) by presenting a full description ofExpand
Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture
Letg be the Lie algebra of a connected reductive groupG over an algebraically closed field of characteristicp>0. Suppose thatG(1) is simply connected andp is good for the root system ofG. Ifp=2,Expand
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