Related papers: The Kauffman skein algebra of the torus
We determine the action of the Kauffman bracket skein algebra of the torus on the Kauffman bracket skein module of the complement of the 3-twist knot. The point is to study the relationship between knot complements and their boundary tori,…
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the $SL_2$ character variety of a topological surface. We realize the skein algebra of the $4$-punctured sphere as the output of a mirror symmetry…
We investigate aspects of Kauffman bracket skein algebras of surfaces and modules of 3-manifolds using quantum torus methods. These methods come in two flavors: embedding the skein algebra into a quantum torus related to quantum Teichmuller…
The ordinary (or classical) Birman-Wenzl-Murakami algebras were initially conceived as an algebraic framework for the Kauffman link invariant. They also appear as centralizer algebras for representations of quantum universal enveloping…
The Kauffman bracket skein algebra of a surface is a generalization of the Jones polynomial invariant for links and plays a principal role in the Witten-Reshetikhin- Turaev topological quantum field theory. However, the multiplicative…
We describe, for a few small examples, the Kauffman bracket skein algebra of a surface crossed with an interval. If the surface is a punctured torus the result is a quantization of the symmetric algebra in three variables (and an algebra…
In this paper we give an alternative basis, $\mathcal{B}_{\rm ST}$, for the Kauffman bracket skein module of the solid torus, ${\rm KBSM}\left({\rm ST}\right)$. The basis $\mathcal{B}_{\rm ST}$ is obtained with the use of the…
Based on the presentation of the Kauffman bracket skein module of the torus given by the third author in previous work, Charles D. Frohman and R\u{a}zvan Gelca established a complete description of the multiplicative operation leading to a…
We compute the Kauffman skein module of the complement of torus knots in S^3. Precisely, we show that these modules are isomorphic to the algebra of Sl(2,C)-characters tensored with the ring of Laurent polynomials.
We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises…
To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a…
A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole or order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the…
For a surface $F$, the Kauffman bracket skein module of $F \times [0,1]$, denoted $K(F)$, admits a natural multiplication which makes it an algebra. When specialized at a complex number $t$, nonzero and not a root of unity, we have…
We determine the dimension of the Kauffman bracket skein module at generic $q$ for mapping tori of the 2-torus, generalising the well-known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild…
We provide a presentation of the Roger and Yang's Kauffman bracket arc algebra for the once-punctured torus and punctured spheres with three or fewer punctures.
We show that the Kauffman bracket skein module of a cylinder over the torus embeds as a subalgebra of the noncommutative torus. Using this we derive nice formulas for the Jones-Wenzl idempotents and analyze the structure of the Kauffman…
We show that the Kauffman bracket skein modules of certain manifolds obtained from integral surgery on a (2,2b) torus link are finitely generated, and list the generators for select examples.
The Temperley-Lieb algebra may be thought of as a quotient of the Hecke algebra of type A, acting on tensor space as the commutant of the usual action of quantum sl(2) on the n-th tensor power of the 2-dimensional irreducible module. We…
We calculate the Roger-Yang skein algebra of the annulus with two interior punctures, $ \mathcal S^{RY}(\Sigma_{0, 2, 2})$, and show there is a surjective homomorphism from this algebra to the Kauffman bracket skein algebra of the closed…
We construct a family of bases for the Kauffman bracket skein module (KBSM) of the product of an annulus and a circle. Using these bases, we find a new basis for the KBSM of $(\beta,2)$-fibered torus as a first step toward developing…