Title: Lie Brackets on Affine Spaces
Speaker: Tomasz Brzeziński
Institution: Swansea University and University of Białystok
Date & Time: March 7, 2024, 20:00–22:00
Location: Zoom ID: 904 645 6677, Password: 2024
We first explore an intrinsic definition of an affine space that does not rely on an underlying vector space, then introduce the concept of a Lie bracket—and thus a Lie algebra—on such an affine space. Since affine spaces lack distinguished elements or additive structure, the traditional notions of antisymmetry and the Jacobi identity must be adapted. We propose suitable modifications of these concepts and illustrate them with examples from matrix algebra and geometry, demonstrating how Lie-theoretic structures can be formulated in affine settings without relying on linear frameworks.
Tomasz Brzeziński is a Professor of Mathematics at Swansea University (UK) and the University of Białystok (Poland). His research spans
algebra (e.g., rings, modules, corings, comodules, Hopf algebras),
noncommutative geometry (algebraic and differential, with a focus on symmetry),
category theory, and
mathematical physics (quantum groups, integrable systems). He is the author or co-author of over 110 papers (with ~45 collaborators) and a monograph. A notable contribution is his revival and advancement of coring theory, which led to the creation of a new AMS classification category for corings and comodules. His work bridges pure algebra with geometric and physical applications, establishing him as a leading figure in noncommutative algebraic structures.
