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Non-representability of cohomology classes by bi-invariant forms (gauge and Kac-Moody groups)

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Abstract

We give a necessary topological condition on a cohomology class of any Lie group

, modelled on a Fréchet space, to be representable by a bi-invariant form on

. As a corollary, we show that if

for somed>0, then there exists a cohomology class in

which cannot be represented by any bi-invariant form. In particular, we conclude that there are ‘many’ cohomology generators, in general, in the case of gauge groups and also Kac-Moody groups which cannot be represented by bi-invariant forms, although, very often, they are representable by left invariant forms.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Shrawan Kumar

  2. Tata Institute of Fundamental Research, 400 005, Colaba, Bombay, India

    Shrawan Kumar

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  1. Shrawan Kumar
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Communicated by A. Jaffe

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Kumar, S. Non-representability of cohomology classes by bi-invariant forms (gauge and Kac-Moody groups). Commun.Math. Phys. 106, 177–181 (1986). https://doi.org/10.1007/BF01454970

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  • DOI: https://doi.org/10.1007/BF01454970

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