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Dirac Cohomology for Lie Superalgebras

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Abstract

Dirac cohomology is a new tool to study representations of semisimple Lie groups and Lie algebras. The aim of this paper is to define a Dirac operator for a Lie superalgebra of Riemannian type and show that this Dirac operator has similar nature as the one for semisimple Lie algebras. As a consequence, we show how to determine the infinitesimal character of a representation by the infinitesimal character of its Dirac cohomology.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China

    Jing-Song Huang

  2. Department of Mathematics, University of Zagreb, Bijenicka 30, PP 335, 10002 Zagreb, Croatia

    Pavle Pandžić

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  1. Jing-Song Huang
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  2. Pavle Pandžić
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Correspondence to Jing-Song Huang or Pavle Pandžić.

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Huang, JS., Pandžić, P. Dirac Cohomology for Lie Superalgebras. Transformation Groups 10, 201–209 (2005). https://doi.org/10.1007/s00031-005-1006-8

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  • DOI: https://doi.org/10.1007/s00031-005-1006-8

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