Cartan Invariants for Witt Lie Superalgebras with p-Characters of Height at Most One

Abstract

We investigate projective modules of the reduced enveloping superalgebra \( U_{\chi }(\frak {g}) \) of the Lie superalgebra \( \frak {g}\) of Witt type with p-character χ of height at most one. We give a formula for the Cartan invariants of \( U_{\chi }(\frak {g}) \) which implies that \( U_{\chi }(\frak {g}) \) has only one block.

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Acknowledgments

We would like to thank anonymous referees, whose careful reading and feedback improve our exposition a lot.

The first named author is supported by NSFC Grant No.11601116, Doctoral Foundation of Hebei Normal University No. L2016B02 and Scientific Research Foundation of Hebei Education Department No. QN2017090. The second named author is supported by NSFC No.11801031 and Beijing Institute of Technology Research Fund Program for Young Scholars.

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Correspondence to Xun Xie.

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Presented by: Alistair Savage

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Duan, F., Xie, X. Cartan Invariants for Witt Lie Superalgebras with p-Characters of Height at Most One. Algebr Represent Theor 24, 287–315 (2021). https://doi.org/10.1007/s10468-020-09947-z

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Keywords

  • Modular representation
  • Cartan invariant
  • Reduced enveloping superalgebra
  • Witt Lie superalgebra

Mathematics Subject Classification (2010)

  • Primary 17B10
  • 17B50; Secondary 17B66
  • 17B70