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Quantum Algebra papers — page 35

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Koszul Theorem for S-Lie coalgebras
For a symmetry braid S-Lie coalgebras, as a dual object to algebras introduced by Gurevich, are considered. For an Young antisymmetrizer an S-exterior algebra is introduced. From this differential…
J. RozanskiDec 7, 1995
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Braided antisymmetrizer as bialgebra homomorphism
For an Yang Baxter operator we show that a bialgebra homomorphism from a free braided tensor bialgebra to a cofree braided shuffle bialgebra is the Woronowicz braided antisymmetrizer. A cofree…
J. RozanskiDec 6, 1995
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Vertex Operator of Uq(Bl) for Level One
In this paper,we give the explicit formulae of vertex operators of Uq(Bl) for level-one as operators on the Fock space. Meanwhile, we point out that the free field realization (by one…
Bai-Qi Jin, Shan-You ZhouDec 5, 1995
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Bicrossproduct Structure of Affine Quantum Groups
We show that the affine quantum group Uq(sl2) is isomorphic to a bicrossproduct central extension C Zχ Uq(Lsl2) of the quantum loop group Uq(Lsl2) by a quantum cocycle χ,…
S. MajidDec 5, 1995
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Fermionic q-Fock Space and Braided Geometry
We write the fermionic q-Fock space representation of Uq(sln) as an infinite extended braided tensor product of finite-dimensional fermionic Uq(sln)-quantum planes or exterior…
S. MajidDec 5, 1995
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On Curvature in Noncommutative Geometry
A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a…
M. Dubois-Violette, J. Madore, T. Masson et al.Dec 4, 1995
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A2 Macdonald polynomials: a separation of variables
In this paper we construct a discrete linear operator K which transforms A2 Macdonald polynomials into the product of two basic 3ϕ2 hypergeometric series with known arguments. The action of…
V. V. MangazeevDec 4, 1995
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Levi-Civita Connections on the Quantum Groups SLq(N), Oq(N) and Spq(N)
For bicovariant differential calculi on quantum groups various notions on connections and metrics (bicovariant connections, invariant metrics, the compatibility of a connection with a metric,…
I. Heckenberger, K. SchmuedgenDec 1, 1995
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On a Universal Invariant of 3-Manifolds
We construct an invariant of 3-manifolds using a modification of the Kontsevich integral and Kirby's calculus. This invariant, as expected in perturbative Chern-Simon theory, takes values in the…
Thang T. Q. Le, Jun Murakami, Tomotada OhtsukiDec 1, 1995
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Multiparametric and coloured extensions of the quantum group GLq(N) and the Yangian algebra Y(glN) through a symmetry transformation of the Yang-Baxter equation
Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general `symmetry transformation' of the `particle conserving' R-matrix is found…
B. Basu-Mallick, P. Ramadevi, R. JagannathanNov 29, 1995
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On Finite Type Invariants of Links and Rational Homology Spheres Derived from the Jones Polynomial and Witten-Reshetikhin-Turaev Invariant
We present a mathematically clean review of our previous results on 1/K expansion of the colored Jones polynomial and on perturbative invariants of 3d rational homology spheres. We also prove that…
L. RozanskyNov 27, 1995
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Cabling the Vassiliev Invariants
We characterise the cabling operations on the weight systems of finite type knot invariants. The eigenvectors and eigenvalues of this family of operations are described over the cable eigenbasis. The…
A. Kricker, B. Spence, I. AitchisonNov 27, 1995
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On The Structure of Quantum Super Groups GLq(m|n)
We show that a quantum super matrix in standard format is invertible if and only if its block matrices of even entries are invertible. We prove the q-analog of the well-known formula for the…
Phung Ho HaiNov 27, 1995
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Some aspects of noncommutative differential geometry
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on…
Michel Dubois-VioletteNov 27, 1995
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Twining characters, orbit Lie algebras, and fixed point resolution
We describe the resolution of field identification fixed points in coset conformal field theories in terms of representation spaces of the coset chiral algebra. A necessary ingredient from the…
J"urgen Fuchs, Bert Schellekens, Christoph SchweigertNov 27, 1995
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Koszul Property and Poincare' Series of Matrix-Bialgebras of Type AN
Bialgebras associated to Yang-Baxter operators satisfying the Hecke equation, are considered. It is shown that they are Koszul algebras. Their Poincare' series are calculated via the…
Phung Ho HaiNov 24, 1995
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Quantization of Poisson Groups
Let Gτ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfel'd structure of Poisson group, let Hτ be its dual Poisson group. By means of…
Fabio GavariniNov 24, 1995
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Dilute Algebras and Solvable Lattice Models
The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and…
Uwe GrimmNov 24, 1995
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A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
We consider the universal solution of the Gervais-Neveu-Felder equation in the Uq(sl2) case. We show that it has a quasi-Hopf algebra interpretation. We also recall its relation to quantum…
O. Babelon, D. BernardNov 23, 1995
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Unitary operator bases and q-deformed algebras
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way,…
D. Galetti, J. T. Lunardi, B. M. Pimentel et al.Nov 23, 1995
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Solution of Constant Yang-Baxter System in the Dimension Two
Complete solution, more precisely, all invertible 4× 4 matrices R,Q that solve Yang--Baxter system related to quantised braided groups, quantum doubles and other systems are given.
L. HlavatyNov 22, 1995
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Multiparameter Deformations of the Algebra gln in Terms of Anyonic Oscillators
Generators of multiparameter deformations Uq;s1,s2,...,sn-1(gln) of the universal enveloping algebra U(gln) are realized bilinearly by means of appropriately generalized form of anyonic…
A. M. Gavrilik, N. Z. IorgovNov 22, 1995
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Quantum Dilogarithm and Tetrahedron Equation
This paper has been temporarily withdrawn for corrections.
S. M. Sergeev, V. V. Bazhanov, V. V. MangazeevNov 21, 1995
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Quantum hyperboloid and braided modules
When a quantum hyperboloid is realized, as a three - parameter algebra , in the usual manner, the following problem arises: what is a ``representation theory'' of this algebra? We construct…
J. Donin, D. Gurevich, V. RubtsovNov 20, 1995
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Higher-Dimensional Algebra I: Braided Monoidal 2-Categories
We begin with a brief sketch of what is known and conjectured concerning braided monoidal 2-categories and their applications to 4d topological quantum field theories and 2-tangles (surfaces embedded…
John C. Baez, Martin NeuchlNov 19, 1995
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