Anticommutation in the Presentations of Theta-Deformed Spheres

TL;DR

This paper introduces a new class of theta-deformed spheres with anticommutation relations, demonstrating that noncommutative Borsuk-Ulam theorems still hold for these structures using K-theory.

Contribution

It presents a novel analogue of theta-deformed spheres with anticommutation relations and proves Borsuk-Ulam theorems in this noncommutative setting using K-theory.

Findings

Noncommutative Borsuk-Ulam theorems hold for these algebras

Anticommutation relations significantly alter the algebraic structure

K-theory is effective in analyzing these noncommutative spaces

Abstract

We consider an analogue of the theta-deformed even spheres, modifying the relations demanded of the self-adjoint generator x in the usual presentation. In this analogue, x is given anticommutation relations with all of the other generators, as opposed to being central. Using even K-theory, we show that noncommutative Borsuk-Ulam theorems hold for these algebras.