On the knot invariants from the Yokonuma-Hecke algebras
Event details
| Date | 31.03.2015 |
| Hour | 15:15 › 17:00 |
| Speaker | Sofia Lambropoulou, Athens |
| Location | |
| Category | Conferences - Seminars |
The Yokonuma-Hecke algebras, $Y_{d,n}(q)$, are quotients of the framed braid group and they include the Iwahori-Hecke algebra, $H_n(q)$, for $d=1$. In the first part of the talk we will discuss the passage from knots to braids and we will present the construction of the 2-variable Jones or Homflypt polynomial for classical knots and links from the algebra $H_n(q)$ and the Ocneanu trace. We shall then introduce the algebras $Y_{d,n}(q)$ and the Juyumaya traces $tr_d$ defined on them. From the traces $tr_d$ we derive invariants for knots and links upon imposing a condition on the trace parameters. The question is how these invariants compare with the Homflypt polynomial. We will show that for knots they are topologically equivalent to the Homflypt polynomial. The case of links is still open.
Practical information
- Informed public
- Free