Celebratio Mathematica — Fuchs — Complete Bibliography

Complete Bibliography

Works connected to Alice Fialowski

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A. Fialowski and D. Fuchs: “Singular deformations of Lie algebras: Example: Deformations of the Lie algebra \( L_1 \),” pp. 77–92 in Topics in singularity theory: V. I. Arnold’s 60th anniversary collection. Edited by A. Khovanskiĭ, A. Varchenko, and V. Vassiliev. AMS Translations. Series 2 180. American Mathematical Society (Providence, RI), 1997. MR 1767113 Zbl 0883.17023 ArXiv q-alg/9706027 incollection

Vladimir Igorevich Arnold	Related
Victor Anatolyevich Vassiliev	Related
Alice Fialowski	Related
Askold Georgievich Khovanskii	Related
Alexander Nicholaevich Varchenko	Related

A. Fialowski and D. Fuchs: “Construction of miniversal deformations of Lie algebras,” J. Funct. Anal. 161 : 1 (1999), pp. 76–110. MR 1670210 Zbl 0944.17015 ArXiv math/0006117 article

We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra. It is known that there is in general no “universal” deformation of a Lie algebra \( L \) with a commutative algebra base \( A \) with the property that for any other deformation of \( L \) with base \( B \) there exists a unique homomorphism \( f:A\to B \) that induces an equivalent deformation. Thus one is led to seek a miniversal deformation. For a miniversal deformation such a homomorphism exists, but is unique only at the first level. If we consider deformations with base \( \operatorname{spec} A \), where \( A \) is a local algebra, then under some minor restrictions there exists a miniversal element. In this paper we give a construction of a miniversal deformation.