Topological obstructions to embedding of a matrix algebra bundle into a trivial one

TL;DR

This paper investigates topological barriers to embedding complex matrix algebra bundles into trivial bundles, linking the problem to principal bundles with groupoids and exploring implications for twisted K-theory.

Contribution

It introduces new topological obstructions for embedding matrix algebra bundles and connects these to principal groupoid bundles and twisted K-theory.

Findings

Identifies specific topological obstructions to embeddings.

Establishes a relation between algebra bundle embeddings and principal groupoid bundles.

Discusses implications for twisted K-theory.

Abstract

In the present paper we describe topological obstructions to embedding of a (complex) matrix algebra bundle into a trivial one under some additional arithmetic condition on their dimensions. We explain a relation between this problem and some principal bundles with structure groupoid. Finally, we briefly discuss a relation of our results to the twisted K-theory.