Representations of the restricted Lie superalgebra p(n)
The center of a quotient of the reduced enveloping algebra of p(n) is studied. By using the obtained results, the restricted representation of p(n) is investigated.
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arXiv subjects
Chaowen Zhang
Publications and source records attributed to Chaowen Zhang.
On the quantum superalgebra U_q(gl(m,n)) and its representations at roots of 1
An purely algebraic proof of the PBW theorem of U_q(gl(m,n)) is given. Lusztig's conjecture is extended to the super case. The Lusztig's tensor product theorem is established.
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On the simplicity of induced modules for reductive Lie algebras. II
A sufficient condition for the simplicity of induced modules of reductive Lie algebras is given.
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On solvable elements in the Weyl algebra
We show that to determine all solvable elements in the Weyl algebra is closely related to the Dixmier's open question. Sufficient conditions for an elements being unsolvable are given, and properties of solvable elements are obtained.
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On the simplicity of Kac modules for the restricted Lie superalgebra gl(m,n)
The polynomial which determine the simplicity of the Kac modules for the restricted Lie superalgebra gl(m,n) is completely determined by a characteristic free approach. Its application on the nonrestricted representation is investigated.
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On the simplicity of induced modules for reductive Lie algebras
The simplicity of the induced modules for reductive Lie algebras over an algebraically closed field of positive characteristic is studied, and a necessary and sufficient condition for the simplicity is given.
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The simplicity of Kac modules for the quantum superalgebra U_q(gl(m,n))
The simplicity of the Kac modules for the quantum superalgebra U_q(gl(m,n)) is studied, and the relation between the representation of U_q(gl(m,n)) and that of U_q(g_{\0}) is investigated.
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Representations for the restricted Lie color algebras
The generalized p-characters for the restricted Lie color are defined. The simplicity of the induced modules for the FP triples are determined. As applications, we have obtained an analogue of the Kac-Weisfiler theorem for the algebraic Lie color algebra cgl(V), also determined the simplicity of the baby Verma modules for cgl(V).
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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 is proved.
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Representations of the restricted Cartan type Lie superalgebra $W(m,n,1)$
Simple modules for the restricted Witt superalgebra $W(m,n,1)$ are considered. Conditions are provided for the restricted and nonrestricted Kac modules to be simple.
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