Making non-trivially associated tensor categories from left coset representatives

TL;DR

This paper constructs non-trivially associated tensor and braided tensor categories from coset representatives, providing explicit algebraic structures and a braided Hopf algebra whose representations form the category.

Contribution

It introduces a novel algebraic framework for tensor categories derived from coset representatives and constructs a braided Hopf algebra with its representations.

Findings

Constructed a non-trivially associated tensor category from coset representatives.

Developed a double construction leading to a braided tensor category.

Explicitly reconstructed a braided Hopf algebra within this framework.

Abstract

The paper begins by giving an algebraic structure on a set of coset representatives for the left action of a subgroup on a group. From this we construct a non-trivially associated tensor category. Also a double construction is given, and this allows the construction of a non-trivially associated braided tensor category. In this category we explicitly reconstruct a braided Hopf algebra, whose representations comprise the category itself.