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Examples of infinity and Lie algebras and their versal deformations

Tom 55 / 2002

Alice Fialowski, Michael Penkava Banach Center Publications 55 (2002), 27-42 MSC: 14D15, 13D10, 14B12, 16S80, 16E40, 17B55, 17B70. DOI: 10.4064/bc55-0-2

Streszczenie

This article explores some simple examples of $L_\infty$ algebras and the construction of miniversal deformations of these structures. Among other things, it is shown that there are two families of nonequivalent $L_\infty$ structures on a $1|1$ dimensional vector space, two of which are Lie algebra structures. The main purpose of this work is to provide a simple effective procedure for constructing miniversal deformations, using the examples to illustrate the general technique. The same method can be applied directly to construct versal deformations of Lie algebras.

Autorzy

  • Alice FialowskiDepartment of Applied Analysis
    Eötvös Loránd University
    Pázmány Péter sétány 1C
    H-1117 Budapest, Hungary
    e-mail
  • Michael PenkavaDepartment of Mathematics
    University of Wisconsin
    Eau Claire
    WI 54702-4004, U.S.A.
    e-mail

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