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Quantum Algebra papers — page 32

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Spinor representations of Uq( o(N))
This is an extension of quantum spinor construction of Uq( gl(n)). We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and…
Jintai DingFeb 12, 1996
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Interesting Relations in Fock Space
Certain non-linear relations between the generators of the (q-deformed) Heisenberg algebra are found. Some of these relations are invariant under quantization and q-deformation.
Alexander TurbinerFeb 8, 1996
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Demazure modules and vertex models: the affine sl(2) case
We characterize, in the case of affine sl(2), the crystal base of the Demazure module Ew() in terms of extended Young diagrams or paths for any dominant integral weight and Weyl group element…
Omar Foda, Kailash C. Misra, Masato OkadoFeb 8, 1996
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Comparing finite type invariants of knots and integral homology 3-spheres
Using elementary counting methods of weight systems for finite type invariants of knots and integral homology 3-spheres, in the spirit of [B-NG], we answer positively three questions raised in [Ga].…
S. GaroufalidisFeb 8, 1996
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The dual (p,q)-Alexander-Conway Hopf algebras and the associated universal T-matrix
The dually conjugate Hopf algebras Funp,q(R) and Up,q(R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf…
R. Chakrabarti, R. JagannathanFeb 7, 1996
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Contractions, Hopf algebra extensions and cov. differential calculus
We re-examine all the contractions related with the Uq(su(2)) deformed algebra and study the consequences that the contraction process has for their structure. We also show using $…
J. A. de Azcarraga, J. C. Perez BuenoFeb 7, 1996
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Cabled Wilson Loops in BF Theories
A generating function for cabled Wilson loops in three-dimensional BF theories is defined, and a careful study of its behavior for vanishing cosmological constant is performed. This allows an…
Alberto S. CattaneoFeb 6, 1996
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The universal Vassiliev invariant for the Lie superalgebra gl(1|1)
We compute the universal weight system for Vassiliev invariants coming from the Lie superalgebra gl(1|1) applying the construction of YB. This weight system is a function from the space of…
José M Figueroa-O'Farrill, Takashi Kimura, Arkady VaintrobFeb 5, 1996
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Semiinfinite cohomology of associative algebras and bar duality
We describe semiinfinite cohomology of associative algebras in terms of Koszul (or bar) duality. Consider an associative algebra A and two its subalgebras B and N such that A=B N as a…
Sergey ArkhipovFeb 5, 1996
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Bispectral algebras of commuting ordinary differential operators
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank N. It combines and unifies the ideas of Duistermaat-Grünbaum and Wilson.…
B. Bakalov, E. Horozov, M. YakimovFeb 4, 1996
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Bäcklund--Darboux transformations in Sato's Grassmannian
We define Bäcklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe…
B. Bakalov, E. Horozov, M. YakimovFeb 3, 1996
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Highest weight modules over W1+infty algebra and the bispectral problem
The present paper establishes a connection between the Lie algebra W1+infty and the bispectral problem. We show that the manifolds of bispectral operators obtained by Darboux transformations on…
B. Bakalov, E. Horozov, M. YakimovFeb 3, 1996
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Homotopy Gerstenhaber algebras and topological field theory
We prove that the BRST complex of a topological conformal field theory is a homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We also suggest a refinement of the original…
Takashi Kimura, Alexander A. Voronov, Gregg J. ZuckermanFeb 2, 1996
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Differential calculus on the quantum Heisenberg group
The differential calculus on the quantum Heisenberg group is conlinebreak structed. The duality between quantum Heisenberg group and algebra is proved.
Piotr Kosinski, Pawel Maslanka, Karol PrzanowskiFeb 2, 1996
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Differential calculi on quantum Minkowski space
The differential calculus on n-dimensional quantum Minkowski space covariant with respect to left action of Kappa-Poincar'e group is constructed and its uniqueness is shown.
Cezary Gonera, Piotr Kosinski, Pawel MaslankaFeb 2, 1996
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A note on geometry of Kappa-Minkowski space
The infinitesimal action of Kappa-Poincar'e group on Kappa-Minkowski space is computed both for generators of Kappa-Poincar'e algebra and those of Woronowicz generalized Lie algebra. The…
Stefan Giller, Cezary Gonera, Piotr Kosinski et al.Feb 2, 1996
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Deformation map for generalized Kappa-Poincar'e and Kappa-Weyl algebras
A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.
Stefan Giller, Cezary Gonera, Michal MajewskiFeb 2, 1996
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The bicovariant differential calculus on the three-dimensional Kappa-Poincar'e group
The bicovariant differential calculus on the three-dimensional Kappa-Poincar'e group and the corresponding Lie-algebra structure are described. The equivalence of this Lie-algebra structure and…
Piotr Kosinski, Michal Majewski, Pawel MaslankaFeb 2, 1996
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Contraction of Algebraical Structures and Different Couplings of Cayley-Klein and Hopf Structures
Contractions (and graded contractions) of Lie algebra, Lie bialgebra and Hopf algebra are discussed. It is noticed the fundamental role of E.Inönü and E.P.Wigner idea of degenerate…
N. A. GromovFeb 2, 1996
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A characterization of coboundary Poisson Lie groups and Hopf algebras
We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G× G on M=G is a Poisson action for an appropriate Poisson structure on M (the structure turns…
S. ZakrzewskiFeb 1, 1996
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Braided Geometry of the Conformal Algebra
We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the q 1 scaling limit of the braided adjoint action or R-commutator of…
S. MajidFeb 1, 1996
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Poisson structures on the Poincare group
An introduction to inhomogeneous Poisson groups is given. Poisson inhomogeneous O(p,q) are shown to be coboundary, the generalized classical Yang-Baxter equation having only one-dimensional right…
S. ZakrzewskiFeb 1, 1996
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Algebraic Bethe Ansatz for XYZ Gaudin model
The eigenvectors of the Hamiltionians of the XYZ Gaudin model are constructed by means of the algebraic Bethe Ansatz. The construction is based on the quasi-classical limit of the corresponding…
E. K. Sklyanin, T. TakebeJan 25, 1996
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Yangians and Capelli identities
We study the image of the universal R-matrix for the Yangian Y(glN) with respect to the evaluation homomorphism of Y(glN) to the enveloping algebra U(glN). We use the fusion procedure as…
Maxim NazarovJan 25, 1996
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An Algorithmic Approach to Classify Knots
I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.
Charilaos AnezirisJan 24, 1996
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