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Lie groupoids and the Frölicher-Nijenhuis bracket

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This paper is dedicated to IMPA’s 60th anniversary.

Abstract

The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frölicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie subalgebra. Along the way, we discuss various examples and different characterizations of multiplicative vector-valued forms.

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Author information

Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Henrique Bursztyn

  2. UFRJ Instituto de Matemática, Av. Athos da Silveira Ramos, 149, CT, Bloco C, 21941-901, Rio de Janeiro, RJ, Brazil

    Thiago Drummond

Authors
  1. Henrique Bursztyn
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  2. Thiago Drummond
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Correspondence to Henrique Bursztyn.

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Bursztyn, H., Drummond, T. Lie groupoids and the Frölicher-Nijenhuis bracket. Bull Braz Math Soc, New Series 44, 709–730 (2013). https://doi.org/10.1007/s00574-013-0031-9

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  • DOI: https://doi.org/10.1007/s00574-013-0031-9

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