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Some properties of generalized reduced Verma modules over $ℤ$ -graded modular Lie superalgebras

Keli Zheng; Yongzheng Zhang — 2017

Czechoslovak Mathematical Journal

We study some properties of generalized reduced Verma modules over $ℤ$ -graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for $ℤ$ -graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules.

Uniqueness of decomposition of pseudo-Riemannian superalgebras

Keli Zheng; Liangyun Chen; Yongzheng Zhang — 2014

Colloquium Mathematicae

This paper is primarily concerned with pseudo-Riemannian superalgebras, which are superalgebras endowed with pseudo-Riemannian non-degenerate supersymmetric consistent bilinear forms. Decompositions of pseudo-Riemannian superalgebras whose left centers are isotropic and whose left centers are not isotropic are investigated.

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Some properties of generalized reduced Verma modules over ℤ -graded modular Lie superalgebras

Uniqueness of decomposition of pseudo-Riemannian superalgebras

Some properties of generalized reduced Verma modules over $ℤ$ -graded modular Lie superalgebras