We generalize Nichita, Popovici and Tanasa solutions of the Braid equation to quasi-Yang-Baxter equation. We define quasi-braided Lie algebras in an additive monoidal category as a natural generalization of Majid’s braided Lie algebra concept. 38 more words

## Tags » Quantum Algebra

#### An Introduction to Coalgebras

I’ve just dumped this here, I wrote it for a project in Luxembourg a few months ago. Its not well edited, and there are errors. I may fix these in the future. 4,375 more words

#### When confusions annihilate

As mathematicians we spend most of our lives confused about something or other. Of course, this is occasionally interrupted by moments of clarity that make it worth it. 410 more words

#### Artin-Wedderburn in fusion categories

In quantum algebra we’re often studying some classical algebraic notion, but instead of working in the category of vector spaces you instead work in a more general tensor category. 694 more words

#### The decline of quantum algebra (QA)

I was browsing through different category listings on the arXiv today and noting the changes in numbers of papers over the years. As you might expect, there are more and more papers being posted to the arXiv every year. 119 more words

#### The Brauer Groupoid

Recall that the Brauer group of a field k consists of central simple algebras over k up to Morita equivalence with the group operation given by tensor product. 1,326 more words

#### Cyclotomic integers, fusion categories, and subfactors (March)

Frank Calegari, Scott Morrison, and I recently uploaded to the arxiv our paper Cyclotomic integers, fusion categories, and subfactors. In this paper we give two applications of cyclotomic number theory to quantum algebra. 358 more words