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Quantum Algebra papers — page 46

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Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras
The characters χμ of nontwisted affine algebras at fixed level define in a natural way a representation R of the modular group SL2(Z). The matrices in the image R(SL2(Z)) are called the…
Terry GannonFeb 3, 1995
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An introduction to quantum groups and non-commutative differential calculus
An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)
J. A. de Azcarraga, F. RodenasFeb 2, 1995
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Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
We investigate the possibility to construct bicovariant differential calculi on quantum groups SOq(N) and Spq(N) as a quantization of an underlying bicovariant bracket.We show that, opposite to…
G. E. Arutuynov, A. P. Isaev, Z. PopowiczFeb 1, 1995
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Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : Uq(sl(3)) and Beyond,
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and…
V. K. Dobrev, P. Truini, L. C. BiedenharnFeb 1, 1995
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Sacler lectures
The series of three lectures given at Tel-Aviv University in 1992: 1. Tensor categories. 2. Quantum groups. 3. Topological (quantum) field theories. Published as the preprint IAS 897-92 of Tel-Aviv…
Joseph BernsteinJan 31, 1995
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Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies.
Hirota bilinear identity for Cauchy-Baker-Akhieser (CBA) kernel is introduced as a basic tool to construct integrable hierarchies containing lattice and q-difference times. Determinant formula for…
L. V. BogdanovJan 29, 1995
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Universal R--matrices for non-standard (1+1) quantum groups
A universal quasitriangular R--matrix for the non-standard quantum (1+1) Poincaré algebra Uziso(1,1) is deduced by imposing analyticity in the deformation parameter z. A family gμ of…
A. Ballesteros, E. Celeghini, F. J. Herranz et al.Jan 27, 1995
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Non-standard quantum (1+1) Poincaré group: a T--matrix approach
The Hopf algebra dual form for the non--standard uniparametric deformation of the (1+1) Poincaré algebra iso(1,1) is deduced. In this framework, the quantum coordinates that generate…
A. Ballesteros, F. J. Herranz, M. A. del Olmo et al.Jan 27, 1995
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Quantum Deformation of igl(n) Algebra on Quantum Space
We study quantum deformed gl(n) and igl(n) algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed gl(n) and igl(n) algebras by a quantum fermionic…
T. Kobayashi, H-T. SatoJan 26, 1995
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Lie-Poisson groups and the Miura transformation
We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng and Mas-Ramos is underpinned by the Lie-Poisson property of the second Gel'fand-Dickey bracket. The supersymmetric…
JM Figueroa-O'Farrill, S StanciuJan 25, 1995
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Lorentz Transformations as Lie-Poisson Symmetries
We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson-Lie group. In so doing we obtain the classical limit of a…
A. Simoni, A. Stern, I. YakushinJan 25, 1995
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Quantum Groups from Path Integrals
Lecture notes from the 1994 CRM-CAP Summer School ``Particles and Fields '94''. Covers material written elsewhere in a more leisurely fashion, including many exercises. Describes…
Daniel S. FreedJan 25, 1995
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First Order Optimum Calculi
A new notion of an optimum first order calculi was introduced in [Borowiec, Kharchenko and Oziewicz, 1993]. A module of vector fields for a coordinate differential is defined. Some examples of…
A. Borowiec, V. K. KharchenkoJan 23, 1995
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Fun(SOq(N))-Isotropic Harmonic Oscillator on the Quantum Euclidean Space RqN
We briefly describe the construction of a consistent q-deformation of the quantum mechanical isotropic harmonic oscillator on ordinary N space.
Gaetano FioreJan 19, 1995
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Is a Knot Classification possible?
The goal of this paper is to discuss the possibility of finding an algorithm that can give all distinct knots up to a desired complexity. Two such algorithms are presented, one based on projections…
Charilaos AnezirisJan 18, 1995
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The fundamental invariant of the Hecke algebra Hn(q) characterizes the representations of Hn(q), Sn, SUq(N) and SU(N)
The irreducible representations (irreps) of the Hecke algebra Hn(q) are shown to be completely characterized by the fundamental invariant of this algebra, Cn. This fundamental invariant is…
J. Katriel, B. Abdesselam, A. ChakrabartiJan 17, 1995
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The quantum superalgebra Uq[osp(1/2n)]: deformed para-Bose operators and root of unity representations
We recall the relation between the Lie superalgebra osp(1/2n) and para-Bose operators. The quantum superalgebra Uq[osp(1/2n)], defined as usual in terms of its Chevalley generators, is shown to…
T. D. Palev, J. Van der JeugtJan 16, 1995
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Quadratic Poisson brackets and Drinfel'd theory for associative algebras
Quadratic Poisson brackets on associative algebras are studied. Such a bracket compatible with the multiplication is related to a differentiation in tensor square of the underlying algebra. Jacobi…
A. A. Balinsky, Yu. M. BurmanJan 16, 1995
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On the universal R-matrix of Uqsl2 at roots of unity
We show that the action of universal R-matrix of affine Uqsl2 quantum algebra, when q is a root of unity, can be renormalized by some scalar factor to give a well defined nonsingular…
T. Hakobyan, A. SedrakyanJan 14, 1995
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Boundary values as Hamiltonian variables. II. Graded Structures
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating…
Vladimir O. SolovievJan 13, 1995
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Coordinate Calculi on Associative Algebras
A new notion of an optimal algebra for a first order coordinate differential was introduced in BKO. Some relevant examples are indicated. Quadratic identities in the optimal algebras and…
A. Borowiec, V. K. KharchenkoJan 13, 1995
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Moonshine Cohomology
We construct a new cohomology functor from the a certain category of quantum operator algebras to the category of Batalin-Vilkovisky algebras. This Moonshine cohomology has, as a…
Bong H. Lian, Gregg J. ZuckermanJan 13, 1995
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Commutative Quantum Operator Algebras
A key notion bridging the gap between quantum operator algebras LZ10 and vertex operator algebras BorFLM is the definition of the commutativity of a pair of quantum…
Bong H. Lian, Gregg J. ZuckermanJan 13, 1995
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Non-Standard KP Evolution and Quantum τ-function
One possible way to fix partly a ``canonical definition'' of τ-functions beyond the conventional KP/Toda framework could be to postulate that evolution operators are always group…
S. Kharchev, A. Mironov, A. MorozovJan 13, 1995
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The Constrained KP Hierarchy and the Generalised Miura Transformation
Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB-1. Whereas most of the…
Javier Mas, Eduardo RamosJan 12, 1995
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