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Algebra, Geometry and Mathematical Physics pp 247–258Cite as

Rigid Current Lie Algebras

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 85))

Abstract

A current Lie algebra is constructed from a tensor product of a Lie algebra and a commutative associative algebra of dimension greater than 2. In this work we are interested in deformations of finite dimensional current Lie algebras and in the problem of rigidity. In particular we prove that a complex finite dimensional current Lie algebra with trivial center is rigid if it is isomorphic to a direct product \(\mathfrak {g}\times \mathfrak {g}\times \cdots \times \mathfrak {g}\) where \(\mathfrak {g}\) is a rigid Lie algebra.

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Authors and Affiliations

  1. Université de Haute Alsace, 68093, Mulhouse, France

    Elisabeth Remm & Michel Goze

Authors
  1. Elisabeth Remm
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  2. Michel Goze
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Corresponding author

Correspondence to Elisabeth Remm .

Editor information

Editors and Affiliations

  1. Informatique et Applications, Université of Haute Alsace, Laboratoire de Mathématiques, Mulhouse, France

    Abdenacer Makhlouf

  2. Tallinn University of Technology, Dept. Mathematics, Tallinn, Estonia

    Eugen Paal

  3. Culture and Communication (UKK) Division of Applied Mathematics, Mälardalen University, The School of Education, Västerås, Sweden

    Sergei D. Silvestrov

  4. Dept. Mathematical Sciences, University of Göteborg, Göteborg, Sweden

    Alexander Stolin

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Remm, E., Goze, M. (2014). Rigid Current Lie Algebras. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_14

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