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Quantum Algebra papers — page 23

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Noninvertibility and ``Semi-'' Analogs of (Super) Manifolds, Fiber Bundles and Homotopies
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to…
Steven DuplijSep 19, 1996
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Algebraic structure of multi-parameter quantum groups
Multi-parameter versions Up(g) and Cp[G] of the standard quantum groups Uq(g) and Cq[G] are considered where G is a semi-simple connected complex algebraic group and g is the Lie algebra of G.…
Timothy J. Hodges, Thierry Levasseur, Margarita ToroSep 19, 1996
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On the Structure of Monodromy Algebras and Drinfeld Doubles
We give a review and some new relations on the structure of the monodromy algebra (also called loop algebra) associated with a quasitriangular Hopf algebra H. It is shown that as an algebra it…
Florian NillSep 18, 1996
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glq(n)-Covariant Multimode Oscillators and q-Symmetric States
In this paper the coherent states and q-symmetric states for glq(n)-covariant multimode oscillator system are investigated.
W-S. ChungSep 18, 1996
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Higher-Dimensional Algebra II: 2-Hilbert Spaces
A 2-Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we define a 2-Hilbert space to be an abelian category enriched over Hilb with a…
John C. BaezSep 17, 1996
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glq(n)-covariant Oscillators and q-Deformed Quantum Mechanics in n Dimensions
In this paper the coherent state for glq(n)-covariant oscillators is constructed and is shown to satisfy the completeness relation. And the q-analogue of quantum mechanics in n dimensions is…
W-S. ChungSep 17, 1996
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Two parameter Deformed Multimode Oscillators and q-Symmetric States
Two types of the coherent states for two parameter deformed multimode oscillator system are investigated. Moreover, two parameter deformed gl(n) algebra and deformed symmetric states are…
W-S. ChungSep 17, 1996
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On Witten-type deformation of osp(1/2) Algebra
In this paper Witten type deformation of osp(1/2) algbera is introduced and its realization and matrix representation are obtained. The matrix representation is shown to be possible only when the…
W-S. ChungSep 17, 1996
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Boundary Solutions of the Classical Yang-Baxter Equation
We define a new class of unitary solutions to the classical Yang-Baxter equation (CYBE). These ``boundary solutions'' are those which lie in the closure of the space of unitary solutions to…
Murray Gerstenhaber, Anthony GiaquintoSep 16, 1996
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Pairing and Quantum Double of Multiplier Hopf Algebras
We define and investigate pairings of multiplier Hopf algebras. It is shown that two dually paired regular multiplier Hopf (*-)algebras A and B yield a quantum double multiplier Hopf…
Bernhard Drabant, Alfons Van DaeleSep 16, 1996
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Generalized differential spaces with dN=0 and the q-differential calculus
We present some results concerning the generalized homologies associated with nilpotent endomorphisms d such that dN=0 for some integer N≥ 2. We then introduce the notion of graded…
Michel Dubois-VioletteSep 13, 1996
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Cartan Pairs
A new notion of Cartan pairs as a substitute of notion of vector fields in noncommutative geometry is proposed. The correspondence between Cartan pairs and differential calculi is established.
A. BorowiecSep 12, 1996
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First Order Calculi with Values in Right--Universal Bimodules
The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and…
A. Borowiec, V. K. Kharchenko, Z. OziewiczSep 11, 1996
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On the q-deformed oscillator algebras:suq(1,1) and suq(2)
We study the relations between q-deformations and q-coherent states of the single oscillator representations for suq(1,1) and suq(2) algebras; Dyson and Holstein-Primakoff type in terms of…
Phillial Oh, Chaiho RimSep 10, 1996
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A three-parameter deformation of the Weyl-Heisenberg algebra: differential calculus and invariance
We define a three-parameter deformation of the Weyl-Heisenberg algebra that generalizes the q-oscillator algebra. By a purely algebraical procedure, we set up on this quantum space two differential…
M. Irac-AstaudSep 9, 1996
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Fusion of q-tensor operators: quasi-Hopf-algebraic point of view
Tensor operators associated with a given quantum Lie algebra admit a natural description in the R-matrix language. Here we employ the R-matrix approach to discuss the problem of fusion of tensor…
Andrei G. BytskoSep 7, 1996
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Invariance quantum groups of the deformed oscillator algebra
A differential calculus is set up on a deformation of the oscillator algebra. It is uniquely determined by the requirement of invariance under a seven-dimensional quantum group. The quantum space and…
J. Bertrand, M. Irac-AstaudSep 5, 1996
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Implications of the Hopf algebra properties of noncommutative differential calculi
We define a noncommutative algebra of four basic objects within a differential calculus on quantum groups: functions, 1-forms, Lie derivatives and inner derivations, as the cross-product algebra…
A. A. VladimirovSep 5, 1996
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The topological realization of a simplicial presheaf
The purpose of this article is to define the topological realization of a simplicial presheaf and to prove (under appropriate conditions) that it is homotopy-invariant under Illusie weak equivalence.…
Carlos SimpsonSep 3, 1996
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The Many Faces of the Chiral Potts Model
In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star-triangle and tetrahedron equations, cyclic…
Helen Au-Yang, Jacques H. H. PerkSep 2, 1996
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The q-calculus for generic q and q a root of unity
The q-calculus for generic q is developed and related to the deformed oscillator of parameter q1/2. By passing with care to the limit in which q is a root of unity, one uncovers the full…
R. S. Dunne, A. J. Macfarlane, J. A. de Azcárraga et al.Aug 30, 1996
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The vector k-constrained KP hierarchy and Sato's Grassmannian
We use the representation theory of the infinite matrix group to show that (in the polynomial case) the n--vector k--constrained KP hierarchy has a natural geometrical interpretation on…
Johan van de LeurAug 30, 1996
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Flexible sheaves
We look at homotopy-coherent diagrams of spaces (after Segal, Leitch, Vogt, Mather, Cordier) over a Grothendieck site; we call these ``flexible presheaves''. After some preliminary materiel,…
Carlos SimpsonAug 29, 1996
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Universal q-differential calculus and q-analog of homological algebra
We recall the definition of q-differential algebras and discuss some representative examples. In particular we construct the q-analog of the Hochschild coboundary. We then construct the universal…
Michel Dubois-Violette, Richard KernerAug 29, 1996
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Self-dual Vertex Operator Superalgebras with Shadows of large minimal weight
The shadow V' of a self-dual vertex operator superalgebra V is defined as the direct sum of the irreducible modules of its even vertex operator subalgebra V(0) not contained in…
Gerald HoehnAug 28, 1996
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