Lie Affgebra Structures on Solvable Lie Algebras.

This talk provides a brief overview of a Lie bracket on affine spaces, known as a Lie affgebra, introduced by K. Grabowska, J. Grabowski, and P. Urbański in 2003. Lie affgebras have been studied in several works by Tomasz Brzeziński and his collaborators. In particular, Lie affgebra structures on various classes of affine spaces of matrices have been investigated. It has been shown that any Lie affgebra is isomorphic to a Lie algebra equipped with an additional element and a specific generalized derivation. Moreover, a close relationship between Lie affgebras and Lie algebras has been established. In this talk, we present Lie affgebra structures on low-dimensional solvable Lie algebras.