We introduce and study a family of groups BBn, called the blocked-braid groups, which are quotients of Artin’s braid groups Bn, and have the corresponding symmetric groups n as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in BBn is Dirac’s Belt Trick - that torsion through 4π is equal to the identity. We show that BBn is finite for n = 1, 2 and 3 but infinite for n > 3.
Blocked-Braid Groups
MAGLIA, DAVIDE;SABADINI, NICOLETTA;WALTERS, ROBERT FRANK CARSLAW
2015-01-01
Abstract
We introduce and study a family of groups BBn, called the blocked-braid groups, which are quotients of Artin’s braid groups Bn, and have the corresponding symmetric groups n as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in BBn is Dirac’s Belt Trick - that torsion through 4π is equal to the identity. We show that BBn is finite for n = 1, 2 and 3 but infinite for n > 3.
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