Dept Math & Stat UiT, Forskningsparken B459
  18 Nov 2025 Tue 14:15-15:45

Henrik Winther (UiT)

"Jet Geometry of the Noncommutative Torus"

We will discuss the jet geometry of the (algebraic and smooth) noncommutative torus and its standard first–order calculus. For each order n, we construct the holonomic jet module J^n(A) and show that it is free as a left A–module with an explicit basis given by prolongations of ordered (q-deformed) trigonometric monomials. In particular, we show that the quantum symmetric tensors consist of q-deformed symmetric tensors, and give explicit formulas for their embedding as the kernel of the canonical jet projection. This yields closed formulas for all prolongations j^n(f) for elements f of A, which in turn gives the algebra of differential operators and the algebra of symbols.