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On the Cohomology of Lie Algebras with an Invariant Inner Product

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Abstract

In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \(\mathbb C\) and \(\mathbb R\) up to dimension 5 and all metric Lie algebras over \(\mathbb C\) in dimension 6. We introduce cyclic and reduced cyclic cohomology to identify their metric deformations.

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Funding

Research of the second author was funded by grants from the University of Wisconsin-Eau Claire.

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Authors and Affiliations

  1. University of Pécs, Eötvös Loránd University, Budapest, Hungary

    Alice Fialowski

  2. University of Wisconsin-Eau Claire, Eau Claire, WI, 54702-4004, USA

    Michael Penkava

Authors
  1. Alice Fialowski
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  2. Michael Penkava
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Correspondence to Alice Fialowski.

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Presented by: Alistair Savage

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Michael Penkava passed away on September 6, 2020.

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Fialowski, A., Penkava, M. On the Cohomology of Lie Algebras with an Invariant Inner Product. Algebr Represent Theor 25, 1107–1131 (2022). https://doi.org/10.1007/s10468-021-10061-x

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  • DOI: https://doi.org/10.1007/s10468-021-10061-x

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