Noncommutative Geometry Seminar

Date: August 26, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Giovanni Landi, Trieste University

Title: Solutions to the quantum YB equation and related deformations

Abstract: We present natural families of coordinate algebras of noncommutative Euclidean spaces and noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an R-matrix which is involutive and satisfies the quantum Yang–Baxter equation. As a consequence they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have spherical manifolds, and noncommutative quaternionic planes as well as noncommutative quaternionic tori. On these there is an action of the classical quaternionic torus SU(2)×SU(2) in parallel with the action of the torus U(1)×U(1) on a complex noncommutative torus.

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