Frobenius algebras derived from the Kauffman bracket skein algebra
نویسندگان
چکیده
منابع مشابه
On Positivity of Kauffman Bracket Skein Algebras of Surfaces
We show that the Chebyshev polynomials form a basic block of any positive basis of the Kauffman bracket skein algebras of surfaces.
متن کاملFundamentals of Kauffman bracket skein modules
Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach algebra situs. When looking at the panorama of skein modules1, we see, past the rolling hills of homologies and homotopies, distant mountains the Kauffman bracket skein module, and farther off in the distance skein modules based on other quantum inva...
متن کاملOn the Kauffman Bracket Skein Module of the Quaternionic Manifold
We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A ±1 ] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z 2-homology of the manifold, we determine that they are linearly independent.
متن کاملThe Kauffman skein algebra of a surface at
We study the structure of the Kauffman algebra of a surface with parameter equal to √ −1. We obtain an interpretation of this algebra as an algebra of parallel transport operators acting on sections of a line bundle over the moduli space of flat SU(2)-connections over the surface. We analyse the asymptotics of traces of curve-operators in TQFT in non standard regimes where the root of unity par...
متن کاملOn the Kauffman Skein Modules
Abstract. Let k be a subring of the field of rational functions in α, s which contains α, s. Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the free k-module generated by isotopy classes of framed links in M modulo the Kauffman skein relations. In the case of k = Q(α, s), the field of rational functions in α, s, we give a basis fo...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2016
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216516500164