Leicester Pure Mathematics Seminar, 14/10/2010
Dima Gurevich (Valenciennes University, France)
Title: Elements of Braided Geometry
Abstract: Braided Geometry means a "non-commutative geometry" based on a generalized (quantum) permutation, which can be associated with a solution of the Quantum Yang-Baxter Equation (the braiding). Many notions of the classical and super-geometries can be naturally generalized in this frameworks. I am going to discuss the braided analogs of the (super-)traces, Lie (super-) algebras, (super-)vector fields etc. Also, I am planning to present recent results concerning braided analogs of oirbits in gl(n)* and explain how a quantization of certain Poisson brackets gives rise to braided objects.