Search results for "Mathematics::Quantum Algebra"
showing 7 items of 77 documents
HOMFLY-PT skein module of singular links in the three-sphere
2012
For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in đ3. Given two invertible elements x, t â R, the HOMFLY-PT skein module of singular links in đ3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.
Compressed Drinfeld associators
2004
Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.
Birman's conjecture for singular braids on closed surfaces
2003
Let M be a closed oriented surface of genus gâĽ1, let Bn(M) be the braid group of M on n strings, and let SBn(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map Ρ : SBn(M)ââ¤[Bn(M)], introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective.
Topological Hopf algebras, quantum groups and deformation quantization
2003
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities and provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described
Kontsevich and Takhtajan construction of star product on the Poisson Lie group GL(2)
2001
Comparing the star product defined by Takhtajan on the Poisson-Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any ''K-star product'') on the same group, we show, by direct computation, that the Takhtajan star product on GL(2) can't be written as a K-star product.
Comparison of frictional resistance between passive self-ligating brackets and slide-type low-friction ligature brackets during the alignment and levâŚ
2019
Background To compare the frictional resistance between passive self-ligating brackets and conventional brackets with low-friction ligature under bracket/archwire and root/bone interface during dental alignment and leveling. Material and methods A tridimensional model of the maxilla and teeth of a patient treated with conventional brackets, and slide ligatures was generated employing the SolidWorks modeling software. SmartClip self-ligating brackets and Logic Line conventional brackets were assembled with slide low-friction ligatures, utilizing archwires with different diameters and alloys used for the alignment and leveling stage. Friction caused during the bracket/archwire interface and sâŚ
Jeu de Taquin and Diamond Cone for so(2n+1, C)
2020
International audience; The diamond cone is a combinatorial description for a basis of a natural indecomposable n-module, where n is the nilpotent factor of a complex semisimple Lie algebra g. After N. J. Wildberger who introduced this notion, this description was achieved for g = sl(n) , the rank 2 semisimple Lie algebras and g = sp (2n).In this work, we generalize these constructions to the Lie algebra g = so(2n + 1). The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they index a basis for the shape algebra of so(2n + 1). Defining the notion of orthogonal quasistandard Young tableaux, we prove that these tableaux describe a basis for a quotient of tâŚ