Examples of infinity and Lie algebras and their versal deformations
Tom 55 / 2002
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.
