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Quantum Algebra papers — page 33

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Semiinfinite cohomology of quantum groups
In this paper we develop a new homology theory of associative algebras called semiinfinite cohomology in a derived category setting. We show that in the case of small quantum groups the zeroth…
Sergey ArkhipovJan 24, 1996
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The hyperbolic volume of knots from quantum dilogarithm
The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number N. By the analysis of particular examples it is argued that for a hyperbolic…
R. M. KashaevJan 23, 1996
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Double quantum groups and Iwasawa decomposition
The double quantum groups are the Hopf algebras underlying the complex quantum groups of which the simplest example is the quantum Lorentz group. They are non- standard quantizations of the double…
Timothy J. HodgesJan 23, 1996
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Differential Calculi and Linear Connections
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that…
Aristophanes Dimakis, J. MadoreJan 23, 1996
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Genealogy of Nonperturbative Quantum-Invariants of 3-Manifolds: The Surgical Family
We study the relations between the invariants τRT, τHKR, and τL of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko, respectively. In particular, we discuss explicitly how…
Thomas KerlerJan 21, 1996
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Quantum groups in higher genus and Drinfeld's new realizations method (sl2 case)
We define double (central and cocentral) extensions of Manin pairs introduced by Drinfeld, attached to curves and meromorphic differentials. We define ``infinite twistings'' of these pairs…
B. Enriquez, V. RubtsovJan 21, 1996
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Finite type link invariants and the non-invertibility of links
We show that a variation of Milnor's μ-invariants, the so-called Campbell-Hausdorff invariants introduced recently by Stefan Papadima, are of finite type with respect to marked…
Xiao-Song LinJan 19, 1996
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Left-Covariant Differential Calculi on SLq(2) and SLq(3)
We study N2-1 dimensional left-covariant differential calculi on the quantum group SLq(N) for which the generators of the quantum Lie algebras annihilate the quantum trace. In this way we…
Konrad Schm"udgen, Axel Sch"ulerJan 19, 1996
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Berezin-Toeplitz Quantization of compact Kaehler manifolds
Invited lecture at the XIV-th workshop on geometric methods in physics, Bialowieza, Poland, July 9-15, 1995. In this lecture results are reviewed obtained by the author together with Martin Bordemann…
Martin SchlichenmaierJan 18, 1996
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Highest weight modules of W1+infty, Darboux transformations and the bispectral problem
We announce a systematic way for constructing bispectral algebras of commuting differential operators of any rank N. It enables us to obtain all previously known classes and examples of bispectral…
B. Bakalov, E. Horozov, M. YakimovJan 18, 1996
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Infinity Algebras and the Homology of Graph Complexes
An A-infinity algebra is a generalization of a associative algebra, and an L-infinity algebra is a generalization of a Lie algebra. In this paper, we show that an L-infinity algebra with an invariant…
Michael PenkavaJan 18, 1996
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On p-Adic Convergence of Perturbative Invariants of Some Rational Homology Spheres
R.~Lawrence has conjectured that for rational homology spheres, the series of Ohtsuki's invariants converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant. We prove this conjecture…
L. RozanskyJan 17, 1996
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Remarks on Quantum Integration
We give a general integration prescription for finite dimensional braided Hopf algebras, deriving the N-dimensional quantum superplane integral as an example. The transformation properties of the…
Chryssomalis ChryssomalakosJan 17, 1996
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On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant
The Turaev-Viro invariant is defined as a certain state sum calculated on an arbitrary simple spine of a 3-manifold. We specify each term of the sum as 0-term, 1-term or 2-term such that each sum of…
Maxim SokolovJan 15, 1996
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The Andrews-Gordon identities and q-multinomial coefficients
We prove polynomial boson-fermion identities for the generating function of the number of partitions of n of the form n=Σj=1L-1 j fj, with f1≤ i-1, fL-1 ≤ i'-1 and…
S. O. WarnaarJan 15, 1996
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Central bialgebras in Braided Categories and Coquasitriangular Structures
Central bialgebras in a braided category are algebras in the center of the category of coalgebras in . On these bialgebras another product can be defined, which plays the role of the…
Phung Ho HaiJan 12, 1996
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Strings, paths, and standard tableaux
For the vacuum sectors of regime-III ABF models, we observe that two sets of combinatorial objects: the strings which parametrize the row-to-row transfer matrix eigenvectors, and the paths which…
S. Dasmahapatra, O. FodaJan 12, 1996
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Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial
We formulate a conjecture about the structure of `upper lines' in the expansion of the colored Jones polynomial of a knot in powers of (q-1). The Melvin-Morton conjecture states that the bottom…
L. RozanskyJan 12, 1996
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Two-parameter deformation of the Poincaré algebra
We examine a two-parameter ( , λ) deformation of the Poincarè algebra which is covariant under the action of SLq(2,C). When λ→ 0 it yields the Poincarè algebra, while in the…
A. Stern, I. YakushinJan 11, 1996
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New Generalized Poisson Structures
New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are provided by conditions on these…
J. A. de Azcarraga, A. M. Perelomov, J. C. Perez BuenoJan 11, 1996
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Bicovariant Calculus on Twisted ISO(N), Quantum Poincare' Group and Quantum Minkowski Space
A bicovariant calculus on the twisted inhomogeneous multiparametric q-groups of the Bn,Cn,Dn type, and on the corresponding quantum planes, is found by means of a projection from the…
Paolo Aschieri, Leonardo CastellaniJan 9, 1996
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Representations of the deformed U(su(2)) and U(osp(1,2)) algebras
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and…
Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis et al.Jan 9, 1996
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Minimal model fusion rules from 2-groups
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group G = 2p+q-5 in the following manner. There is a partition $G = P1…
Fusun Akman, Alex J. Feingold, Michael D. WeinerJan 5, 1996
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On representations of the elliptic quantum group Eτ,η(sl2)
We describe representation theory of the elliptic quantum group Eτ,η(sl2). It turns out that the representation theory is parallel to the representation theory of the Yangian Y(sl2) and the…
Giovanni Felder, Alexander VarchenkoJan 3, 1996
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An Invariant of Integral Homology 3-Spheres Which Is Universal For All Finite Type Invariants
In [LMO] a 3-manifold invariant Ω(M) is constructed using a modification of the Kontsevich integral and the Kirby calculus. The invariant Ω takes values in a graded Hopf algebra of Feynman…
Thang T. Q. LeJan 2, 1996
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