Algebra Seminar

I will describe the solutions of Garside (1969) and Brieskorn and Saito (1972) to the word, division, conjugacy and embedding problems of positive braid monoids. Their techniques can be extended to a larger class of monoids, as I will outline. When such a monoid has a `fundamental element' (something like the longest word in a Coxeter group), it can be naturally embedded in a group or related monoid, and the solution to the word problem in the monoid gives a solution to the word problem in the group. Results regarding

• singular braid monoids, and
• braid groups of complex reflection groups