The algebra of strand splitting. II. A presentation for the braid group on one strand

摘要

The author previously introduced groups BV and BV as braided versions of groups introduced by Richard J. Thompson and as having connections to braided tensor categories. Here we show that BV and BV are finitely presented by exhibiting finite presentations for them. We show that these groups are "Artinifications" of the older Thompson groups V and V by showing that presentations for V and V can be obtained from presentations for BV and BV by adding relations that trivialize the squares of the generators of the latter groups.