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Quantum Algebra papers — page 37

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Crossed modules and quantum groups in braided categories
Let A be a Hopf algebra in a braided category C. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition.…
Yu. N. BespalovOct 12, 1995
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On braided FRT-construction
Fully braided analog of Faddeev-Reshetikhin-Takhtajan construction of quasitriangular bialgebra A(X,R) is proposed. For given pairing C factor-algebra A(X,R;C) is a dual quantum braided group.…
Yuri BespalovOct 12, 1995
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Deformed Minkowski spaces: clasification and properties
Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz…
J. A. de Azcarraga, F. RodenasOct 11, 1995
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On Reduced Q-Functions
Schur's Q-functions with reduced variables are discussed by employing a combinatorics of strict partitions. They are called reduced Q-functions. We give a description of the linear relations…
Tatsuhiro Nakajima, Hiro-Fumi YamadaOct 11, 1995
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The Einstein Action for Algebras of Matrix Valued Functions - Toy Models
Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix…
Piotr M. HajacOct 6, 1995
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Hopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories
Hopf (bi-)modules and crossed modules over a bialgebra B in a braided monoidal category C are considered. The (braided) monoidal equivalence of both categories is proved provided B is a Hopf algebra…
Yuri Bespalov, Bernhard DrabantOct 6, 1995
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Vassiliev invariants I: Braid groups and rational homotopy theory
We get a detailed account of Vassiliev type invariants starting with Chen's theory of iterated integrals and Malcev's completion of discrete groups. The canonical injection of the group of…
Louis FunarOct 6, 1995
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Crystallized Peter-Weyl type decomposition for level 0 part of modified quantum algebra Uq(sl2)0
We shall give some criteria for the existence of the Peter-Weyl type decomposition for modified quantum algebra, which is motivated by the fact that modified quantum algebra has commutative two…
Toshiki NakashimaOct 4, 1995
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Unified view of multimode algebras with Fock-like representations
A unified view of general multimode oscillator algebras with Fock-like representations is presented.It extends a previous analysis of the single-mode oscillator algebras.The expansion of the…
Stjepan Meljanac, Marijan MilekovicOct 4, 1995
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Quantum Lie algebras of type An
It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, defined by means of axioms similar to Woronowicz's., This gives rise to Lie algebra-like generators and…
Volodimir Lyubashenko, Anthony SudberyOct 3, 1995
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Finite type invariants of integral homology 3-spheres: A survey
This is a survey on the current status of the study of finite type invariants of integral homology 3-spheres based on lectures given in the workshop on knot theory at Banach International Center of…
Xiao-Song LinOct 3, 1995
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Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras
A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special…
C. FrønsdalOct 2, 1995
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Comment on ``Generalized q-oscillators and their Hopf structures''
In a recent paper (1994 J.\ Phys.\ A: Math.\ Gen.\ 27 5907), Oh and Singh determined a Hopf structure for a generalized q-oscillator algebra. We prove that under some general…
C. Quesne, N. VansteenkisteOct 2, 1995
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Matched differential calculus on the quantum groups GLq(2,C),SLq(2,C),Cq(2|0)
We proposed the construction of the differential calculus on the quantum group and its subgroup with the property of the natural reduction: the differential calculus on the quantum group GLq(2,C)…
V. P. Akulov, V. D. GershunSep 29, 1995
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On equivariant quantum cohomology
Using the Kontsevich's moduli space of stable maps, we define the equivariant quantum cohomology for generalized flag varieties and make a rigorous computation of quantum cohomology of flag…
Bumsig KimSep 27, 1995
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On Finite Type 3-manifold invariants IV: Comparison of Definitions
This paper compares the definitions of finite-type invariants due to Ohtsuki and to Garoufalidis, showing that, residually, type 3m of the former equals type m of the latter. It also shows that type…
Stavros Garoufalidis, Jerome LevineSep 27, 1995
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TQFT and Whitehead's manifold
The aim of this note is to derive some invariants at infinity for open 3-manifolds in the framework of Topological Quantum Field Theories. These invariants may be used to test if an open manifold is…
Louis FunarSep 26, 1995
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Vertex operator algebras associated to admissible representations of sl2
The admissible modules for sl2 are studied from the point of view of vertex operator algebra. If l is rational such that l+2=p q for some coprime positive integers p 2 and…
Chongying Dong, Haisheng Li, Geoffrey MasonSep 25, 1995
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Vertex operator algebras associated to modular invariant representations for A1 (1)
We investigate vertex operator algebras L(k,0) associated with modular-invariant representations for an affine Lie algebra A1 (1) , where k is 'admissible' rational number. We show…
Drazen Adamovic, Antun MilasSep 22, 1995
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SLq(N) differential calculus from the differential calculus on GLq(N)
We show that the Faddeev-Pyatov SLq(N) differential algebra is a subalgebra of the GLq(N) differential algebra constructed by Schupp, Watts and Zumino.
A. P. IsaevSep 22, 1995
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Algebras and Hopf Algebras in Braided Categories
This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, aswell as colour-Lie…
S. MajidSep 22, 1995
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Some Remarks on the Representation of the Generalized Deformed Oscillator Algebra
The classification of the representations of the generalized deformed oscillator algebra is given together with several comments about possibility of introducing a coproduct structure in some type of…
V. V. Borzov, E. V. Damaskinsky, S. B. YegorovSep 20, 1995
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Vector bundles on elliptic curve and Sklyanin algebras
In [4] we introduce the associative algebras Qn,k(,τ). Recall the definition. These algebras are labeled by discrete parameters n,k; n,k are integers n>k>0 and n and k have not…
B. L. Feigin, A. V. OdesskiiSep 20, 1995
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Chern-Simons theory on a lattice and a new description of 3-manifolds invariants
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge…
E. BuffenoirSep 19, 1995
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Psi - Vectors for Three Dimensional Models
In this paper we apply the method of psi-vectors to three dimensional statistical models. This method gives the correspondence between the Bazhanov -- Baxter model and its vertex formulation.…
S. M. Sergeev, H. E. Boos, V. V Mangazeev et al.Sep 18, 1995
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