Markov trace on the algebra of braids and ties

Francesca Aicardi, Jesus Juyumaya

Published 2014-08-25Version 1

We prove that the so-called "algebra of braids and ties" supports a Markov trace. Further, by using this trace in the Jones recipe we define invariant polynomials for classical knots and singular knots. Our invariants have three parameters. The invariant for classical knots is an extension of the Homflypt polynomial and the invariant for singular knots is an extension of an invariant of singular knots defined by the second author and S. Lambropoulou.