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Quantum Algebra papers — page 20

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Bicharacters, braids and Jacobi identity
For an abelian group G we consider braiding in a category of G-graded modules MkG given by a bicharacter χon G. For (G,χ)-bialgebra A in MkG an analog of Lie bracket is defined. This…
Jerzy RozanskiNov 22, 1996
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Enhancing an R-matrix
In order to construct a representation of the tangle category one needs an enhanced R-matrix. In this paper we define a sufficient and necessary condition for enhancement that can be checked easily…
Marco Arien MackaayNov 21, 1996
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Quasi Hopf Deformations of Quantum Groups
The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard…
Christian FrønsdalNov 21, 1996
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Calogero-Moser pairs and the Airy and Bessel bispectral involutions
Explicit formulae are given for the Airy and Bessel bispectral involutions, in terms of Calogero-Moser pairs. Hamiltonian structure of the motion of the poles of the operators is discussed.
Mitchell RothsteinNov 21, 1996
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The Hopf algebra isomorphism between kappa-Poincare algebra in the case g00=0 and "null plane" quantum Poincare algebra
The Hopf algebra isomorphism between kappa-Poincare algebra defined by P.Kosinski and P.Maslanka in the case g00=0 and "null plane" quantum Poincare algebra by A.Ballesteros, F.J.Herranz…
Karol PrzanowskiNov 21, 1996
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Structure And Representations Of The Quantum General Linear Supergroup
The structure and representations of the quantum general linear supergroup GLq(m|n) are studied systematically by investigating the Hopf superalgebra Gq of its representative functions. Gq is…
R. B. ZhangNov 21, 1996
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C*-algebraic quantum groups arising from algebraic quantum groups
We associate to an algebraic quantum group a C*-algebraic quantum group and prove that this C*-algebraic quantum group satisfies an upcoming definition of Masuda, Nakagami & Woronowicz.
Johan Kustermans, Alfons Van DaeleNov 20, 1996
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Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators
This talk reports on results on the deformation quantization (star products) and on approximative operator representations for quantizable compact K"ahler manifolds obtained via Berezin-Toeplitz…
Martin SchlichenmaierNov 19, 1996
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Minimal Uncertainty States For Quantum Groups
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group…
R. Delbourgo, R. B. ZhangNov 19, 1996
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Lickorish Invariant And Quantum OSP(1|2)
Lickorish's method for constructing topological invariants of 3 - manifolds is generalized to the quantum supergroup setting. An invariant is obtained by applying this method to the Kauffman…
R. B. Zhang, H. C. LeeNov 19, 1996
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Topics in hidden symmetries. IV
This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author's (based on the…
Denis V. JurievNov 18, 1996
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Factorizable D-modules
A braided tensor category FMκ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category FSq of factorizable sheaves from q-alg/9604001. This category is…
Sergei Khoroshkin, Vadim SchechtmanNov 18, 1996
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Actions of Pointed Hopf Algebras
Action of finite-dimensional Hopf algebra H on commutative k-algebra A is considered. As a generalization of the well-known fact for finite groups S. Montgomery raised a problem in 1993 whether…
Vyacheslav Artamonov, Alexander TotokNov 14, 1996
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Knot Theory of Coxeter type B and its physical applications
Braid groups may be defined for every Coxeter diagram. Artin's braid group is of type A. Analogs of Temperley-Lieb, Hecke and Birman-Wenzl algebras exist for B-type. Our general hypothethis is…
Reinhard Häring-OldenburgNov 14, 1996
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A Generalization of Uh(sl(2)) via Jacobian Elliptic Function
A two-parametric generalization of the Jordanian deformation Uh (sl(2)) of sl(2) is presented. This involves Jacobian elliptic functions. In our deformation U(h,k)(sl(2)), for k2=1 one…
A. ChakrabartiNov 13, 1996
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Induced Hopf stucture and irreducible representations of an elliptic Uq,p(sl(2)) via a nonlinear map
Shiraishi's two parameter generalization of Uq(sl(2)) to Uq,p(sl(2)) involving an elliptic function is considered. The generators are mapped non-linearly on those of Uq(sl(2)).…
A. ChakrabartiNov 13, 1996
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On boson algebras as Hopf algebras
Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding…
I Tsohantjis, A Paolucci, P D JarvisNov 13, 1996
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Variation on a theme of Selberg integral
In this paper we calculate some Generalized Selberg integrals. The answer is expressed in terms of Γ-functions. Integrals of this type serve as normalization constants or directly via undoing 2-D…
A. Kazarnovski-KrolNov 12, 1996
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BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials
We consider 3-parametric polynomials which replace the A-series interpolation Macdonald polynomials in the BC case. For these polynomials, we prove: an integral representation, a combinatorial…
Andrei OkounkovNov 11, 1996
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Vertex Operators - From a Toy Model to Lattice Algebras
Within the framework of the discrete Wess-Zumino-Novikov-Witten theory we analyze the structure of vertex operators on a lattice. In particular, the lattice analogues of operator product expansions…
A. G. Bytsko, V. SchomerusNov 11, 1996
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Finite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity
We study irreducible unitary of Uq(SO(2,1)) and Uq(SO(2,3)) for q a root of unity, which are finite dimensional. Among others, unitary corresponding to all classical one-particle…
Harold SteinackerNov 8, 1996
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Weak C* Hopf Symmetry
Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with…
K. -H. RehrenNov 7, 1996
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On inner product in modular tensor categories. II. Inner product on conformal blocks and affine inner product identities
This is the second part of the paper (the first part is published in Jour. of AMS, vol.9, 1135--1170, q-alg/9508017). In the first part, we defined for every modular tensor category (MTC) inner…
Alexander KirillovNov 7, 1996
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Braided Geometry and the Inductive Construction of Lie Algebras and Quantum Groups
Double-bosonisation associates to a braided group in the category of modules of a quantum group, a new quantum group. We announce the semiclassical version of this inductive construction.
S. MajidNov 5, 1996
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On the q-analog of homological algebra
This is an attempt to generalize some basic facts of homological algebra to the case of "complexes" in which the differential satisfies the condition dN=0 instead of the usual d2=0.…
M. M. KapranovNov 4, 1996
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