Krzysztof Radziszewski
Affinization of algebraic structures: Lie algebras
By affinization we mean a process which converts an algebraic structure with a nullary operation (i.e., in which a chosen element plays special role) into one which has no nullary operations, but is such that by a free choice of any element it is retracted to the original structure. The prime example of this procedure is the conversion of groups into heaps.
In this talk we will show how to define a Lie bracket on an affine space to obtain a Lie affgebra. We will present the main theorem which states that to construct a Lie affgebra for a given Lie algebra we need generalized derivations and an algebra element. We will consider a particular class of derivation-type Lie affgebras and then say a few words about the classification of low-dimensional Lie affgebras. The talk is based on joint work with Tomasz Brzeziński and Ryszard Andruszkiewicz.
