A Noncommutative Borsuk-Ulam Theorem for Natsume-Olsen Spheres
Abstract
Natsume-Olsen noncommutative spheres are C*-algebras which generalize C(S^k) when k is odd. These algebras admit natural actions by finite cyclic groups, and if one of these actions is fixed, any equivariant homomorphism between two Natsume-Olsen spheres of the same dimension induces a nontrivial map on odd K-theory. This result is an extended, noncommutative Borsuk-Ulam theorem in odd dimension, and just as in the topological case, this theorem has many (almost) equivalent formulations in terms of theta-deformed spheres of arbitrary dimension. In addition, we present theorems on graded Banach algebras, motivated by algebraic Borsuk-Ulam results of A. Taghavi.
Keywords
Cite
@article{arxiv.1503.01822,
title = {A Noncommutative Borsuk-Ulam Theorem for Natsume-Olsen Spheres},
author = {Benjamin Passer},
journal= {arXiv preprint arXiv:1503.01822},
year = {2019}
}
Comments
26 pages. Version 4 has significantly simplified arguments. To appear in Journal of Operator Theory