A braids and ties algebra of type B

We introduce an algebra of braids and ties (or bt-algebra) of type B. In analogy to the construction of the bt-algebra of type A, we define this bt–algebra of type B through a framization of the Hecke algebra of type B. We find a basis for it, a faithful tensorial representation, and we prove that i...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2020-01, Vol.224 (1), p.1-32
Main Author: Flores, Marcelo
Format: Article
Language:English
Subjects:
Braids of type B
bt–algebra of type B
Framization
Knots and links in solid torus
Link invariants
Markov trace
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Summary:We introduce an algebra of braids and ties (or bt-algebra) of type B. In analogy to the construction of the bt-algebra of type A, we define this bt–algebra of type B through a framization of the Hecke algebra of type B. We find a basis for it, a faithful tensorial representation, and we prove that it supports a Markov trace, from which we derive invariants of classical links in the solid torus.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2019.04.011