Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 699-713, 2017

Some properties of generalized reduced Verma modules over $\mathbb{Z}$-graded modular Lie superalgebras

Keli Zheng, Yongzheng Zhang

Received February 5, 2016.   First published July 13, 2017.

Keli Zheng, Department of Mathematics, Northeast Forestry University, 26 Hexing Road, Xiangfang, Harbin, 150040, Heilongjiang, P. R. China, e-mail: zhengkl561@nenu.edu.cn, Yongzheng Zhang, School of Mathematics and Statistics, Northeast Normal University, Nanguan Qu, Changchun, 130024, Jilin Sheng, P. R. China, e-mail: zhyz@nenu.edu.cn

Abstract: We study some properties of generalized reduced Verma modules over $\mathbb{Z}$-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 $\mathbb{Z}$-graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules.

Keywords: modular Lie superalgebra; generalized reduced Verma module; coinduced module; invariant form; mixed product

Classification (MSC 2010): 17B50, 17B10, 17B05

DOI: 10.21136/CMJ.2017.0050-16

Full text available as PDF.


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