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Algebras and Representation Theory

, Volume 21, Issue 6, pp 1395–1409 | Cite as

On Irreducible Representations of the Zassenhaus Superalgebras with p-Characters of Height 0

  • Yu-Feng Yao
  • Temuer Chaolu
Article

Abstract

Let n be a positive integer, and \(\mathfrak {A}(n)=\mathbb {F}[x]/(x^{p^{n}})\), the divided power algebra over an algebraically closed field \(\mathbb {F}\) of prime characteristic p > 2. Let π(n) be the tensor product of \(\mathfrak {A}(n)\) and the Grassmann superalgebra \(\bigwedge (1)\) in one variable. The Zassenhaus superalgebra \(\mathcal {Z}(n)\) is defined to be the Lie superalgebra of the special super derivations of the superalgebra π(n). In this paper we study simple modules over the Zassenhaus superalgebra \(\mathcal {Z}(n)\) with p-characters of height 0. We give a complete classification of the isomorphism classes of such simple modules and determine their dimensions. A sufficient and necessary condition for the irreducibility of Kac modules is obtained.

Keywords

The Zassenhaus superalgebra Irreducible module p-character Height 

Mathematics Subject Classification 2010

17B10 17B50 17B70 

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Notes

Acknowledgements

The authors would like to express their sincere gratitude to the referee for his/her valuable suggestions and comments which help us to improve the exposition of this paper.

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Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiChina

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