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Quantum Algebra papers — page 19

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On Lie Algebras in the Category of Yetter-Drinfeld Modules
The category of Yetter-Drinfeld modules over a Hopf algebra (with bijektive antipode over a field) is a braided monoidal category. Given a Hopf algebra in this category then the primitive elements of…
Bodo PareigisDec 17, 1996
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Symmetrizable Quantum Affine Superalgebras And Their Representations
Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight…
R. B. ZhangDec 17, 1996
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Cohomological Properties of Differential Calculi on Hopf Algebras
In this report we give an intrinsic treatment of the results we developed in a previous work connecting the differential calculi on Hopf algebras to the Drinfeld double. In the first place we recover…
F. Bonechi, R. Giachetti, R. Maciocco et al.Dec 14, 1996
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Paths, Demazure Crystals and Symmetric Functions
We review the path realization of Demazure crystals and discuss Demazure characters in the light of symmetric functions.
A. Kuniba, K. C. Misra, M. Okado et al.Dec 13, 1996
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Quommutator deformations of osp(2,2)
We analyse the Witten-Woronowicz's type deformations of the Lie superalgebra osp(2,2) and obtain a deformation parametrized by three independent parameters. For some of these algebras, finite…
Yves BrihayeDec 12, 1996
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Bott - Borel - Weil Construction For Quantum Supergroup Uq(gl(m|n))
The finite dimensional irreducible representations of the quantum supergroup Uq(gl(m|n)) are constructed geometrically using techniques from the Bott - Borel - Weil theory and vector coherent…
R. B. ZhangDec 12, 1996
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Holomorphic deformation of Hopf algebras and applications to quantum groups
In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed…
Markus J. Pflaum, Martin SchottenloherDec 11, 1996
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Integral soluitons of q-difference equations of the hypergeometric type with |q|=1
Two integral solutions of q-difference equations of the hypergeometric type with |q|=1 are constructed by using the double sine function. One is an integral of the Barnes type and the other is of the…
Michitomo Nishizawa, Kimio UenoDec 11, 1996
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Crossed Product Structure of Quantum Euclidean Groups
It is shown that quantum Euclidean groups Eq(2), Eκ(2) and Eκ(3) have the structure of generalised crossed products.
Tomasz BrzezinskiDec 10, 1996
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Drinfel'd Twists and Algebraic Bethe Ansatz
We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the…
J. M. Maillet, J. Sanchez de SantosDec 10, 1996
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Vertex operator algebras and associative algebras
Let V be a vertex operator algebra. We construct a sequence of associative algebras An(V) (n=0,1,2,...) such that An(V) is a quotient of An+1(V) and a pair of functors between the category of…
Chongying Dong, Haisheng Li, Geoffrey MasonDec 5, 1996
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Deformations of (Bi) tensor Categories
We define the cohomology and formal deformation theories for algebra and bialgebra categories. We suggest some approaches to finding nontrivial deformations of the categories associated to the…
Louis Crane, David YetterDec 5, 1996
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Hopf algebra extension of a Zamolochikov algebra and its double
The particles with a scattering matrix R(x) are defined as operators Φi(z) satisfying the relation Ri,jj',i'(x1/x2) Φi'(x1)Φj'(x2)= Φi(x2)Φj(x1). The algebra…
Jintai DingDec 4, 1996
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Quantum current operators (III): Commutative quantum current operators, semi-infinite construction and functional models
We construct a commutative current operator x+(z) inside Uq( sl(2)). With this operator and the condition of quantum integrability on the quantum current of $Uq(…
Jintai Ding, Boris FeiginDec 4, 1996
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Complex suq(2) Dynamical Symmetry, Limiting Cases and 1-Dimensional Potential Realisation
Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf…
A. Ludu, W. ScheidDec 4, 1996
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Generalized KdV Equation for Fluid Dynamics and Quantum Algebras
We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a…
A. Ludu, R. A. Ionescu, W. GreinerDec 3, 1996
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Nullification Writhe and Chirality of Alternating Links
In this paper, we show how to split the writhe of reduced projections of oriented alternating links into two parts, called nullification writhe, or wx, and remaining writhe, or wy, such that the sum…
Corinne CerfDec 2, 1996
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Quasi-Continuous Symmetries of Non-Lie Type
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with…
Andrei Ludu, Walter GreinerDec 2, 1996
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Non-Symmetric Jack Polynomials and Integral Kernels
We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange…
T. H. Baker, P. J. ForresterDec 1, 1996
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On Lie Algebras in Braided Categories
The set of primitive elements of a Hopf algebra in the braided category of group graded vector spaces (with a commutative group) carry the structure of a generalized Lie algebra. In particular the…
Bodo PareigisDec 1, 1996
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Quantum Deformation of the WN Algebra
We review the WN algebra and its quantum deformation, based on free field realizations. The (quantum deformed) WN algebra is defined through the (quantum deformed) Miura transformation, and its…
H. Awata, H. Kubo, S. Odake et al.Dec 1, 1996
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Tensor ideals in the category of tilting modules
We study the tensor category of tilting modules over a quantum group Uq with divided powers. The set X+ of dominant weights is a union of closed alcoves w numbered by the elements…
V. OstrikNov 27, 1996
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Combinatorial Structure of Finite Dimensional Representations of Yangians: the Simply-Laced Case
We compute the decomposition of representations of Yangians into g-modules for simply-laced Lie algebras g. The decomposition has an interesting combinatorial tree structure. Results depend on a…
Michael KleberNov 25, 1996
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Boson representations, non-standard quantum algebras and contractions
A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of sl(2,) which directly provides its infinite and finite dimensional…
Angel Ballesteros, Francisco J. Herranz, Javier NegroNov 25, 1996
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Quantum toroidal algebras and their vertex representations
We change the definition of the vertex representations. As a result the vertex representations has one parameter.
Yoshihisa SaitoNov 22, 1996
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