Tomasz Brzeziński

Vector space valued Lie brackets on affine spaces or Lie affgebras were introduced by Grabowska, Grabowski and Ubrański in early 2000s. 

With the recent developments of heaps and heaps of modules, it has become clear how to extend this definition to affine space valued Lie brackets on affine spaces. 

In this talk I will present basic elements of the Lie affgebra theory, focusing on the two-way relationship between Lie affgebras and Lie algebras which allows one to view Lie affgebras as Lie algebra fibered affine spaces. 

The results presented in this talk have been obtained in collaboration with Ryszard Andruszkiewicz, James Papworth and Krzysztof Radziszewski.