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

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Abstract

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.

Keywords

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

MSC 2010

17B50 17B10 17B05 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsNortheast Forestry UniversityXiangfang, Harbin, HeilongjiangP.R. China
  2. 2.School of Mathematics and StatisticsNortheast Normal University, Nanguan QuChangchun, Jilin ShengP.R. China

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