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Quantum Algebra papers — page 8

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Doubles of Quasi-Quantum Groups
Drinfeld showed that any finite dimensional Hopf algebra extends to a quasitriangular Hopf algebra (), the quantum double of . Based on the construction of a so--called diagonal crossed…
Frank Hausser, Florian NillAug 22, 1997
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Anyonic Lie Algebras
We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.
S. MajidAug 21, 1997
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simplicial cohomology of orbifolds
For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for…
Ieke Moerdijk, Dorette A PronkAug 21, 1997
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Quantum groupoids and deformation quantization
The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a…
Ping XuAug 19, 1997
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Applications of the lantern identity
The purpose of this note is to unify the role of the lantern identity in the proof of several finiteness theorems. In particular, we show that for every nonnegative integer m, the vector space (over…
Stavros GaroufalidisAug 19, 1997
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Symmetries in the fourth Painleve equation and Okamoto polynomials
We propose a new representation of the fourth Painlevé equation in which the A(1)2-symmetries become clearly visible. By means of this representation, we clarify the internal relation between…
Masatoshi Noumi, Yasuhiko YamadaAug 19, 1997
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Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the…
Gaetano FioreAug 18, 1997
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Classification of irreducible modules of W3 algebra with c = -2
We construct irreducible modules Vα, α∈ over W3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W3 algebra with c =…
Weiqiang WangAug 17, 1997
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Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups
The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation introduced by Gervais, Neveu, and Felder. The QDYB equation and its…
Pavel Etingof, Alexander VarchenkoAug 16, 1997
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A Note on First Order Differential Calculus on Quantum Principal Bundles
The relationship between the exactness of a first order differential calculus on a comodule algebra P and the Galois property of P is investigated.
Piotr M. HajacAug 14, 1997
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Higher Order Differential Calculus on SLq(N)
Let Γ be an N2-dimensional bicovariant first order differential calculus on a Hopf algebra SLq(N). There are three possibilities to construct a differential Z-graded Hopf algebra Γ…
I. Heckenberger, A. SchuelerAug 13, 1997
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Star Products for integrable Poisson Structures on R3
We prove the existence of a deformation quantization for integrable Poisson structures on R3 and give a generalization for a special class of three dimensional manifolds.
C. NowakAug 12, 1997
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Applications of braided endomorphisms from conformal inclusions
We give three applications of general theory about braided endomorphisms from conformal inclusions developed previously by us. The first is an example of subfactors associated with conformal…
Feng XuAug 12, 1997
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Coalgebra Extensions and Algebra Coextensions of Galois Type
The notion of a coalgebra-Galois extension is defined as a natural generalisation of a Hopf-Galois extension. It is shown that any coalgebra-Galois extension induces a unique entwining map ψ…
Tomasz Brzezinski, Piotr M. HajacAug 9, 1997
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String field theory and quantum groups. I. Quantum group structures in geometric quantization of a self-interacting string field
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to…
Denis V. JurievAug 8, 1997
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W1+ ∞ algebra, W3 algebra, and Friedan-Martinec-Shenker bosonization
We show that the vertex algebra W1+ ∞ with central charge -1 is isomorphic to a tensor product of the simple W3 algebra with central charge -2 and a Heisenberg vertex algebra generated by a…
Weiqiang WangAug 7, 1997
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On Matrix Quantum Groups of type An
Given a Hecke symmetry R, one can define a matrix bialgebra ER and a matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups…
Phung Ho HaiAug 5, 1997
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Deformations of W-algebras associated to simple Lie algebras
Deformed --algebra q,t() associated to an arbitrary simple Lie algebra is defined together with its free field realizations and the screening operators. Explicit formulas are given…
Edward Frenkel, Nicolai ReshetikhinAug 4, 1997
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Diffeomorphism-Invariant Spin Network States
We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a…
John C. Baez, Stephen SawinAug 4, 1997
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Diagonal Crossed Products by Duals of Quasi-Quantum Groups
Let be a (weak) quasi-Hopf algebra. Using a two-sided -coaction on an algebra , we construct what we call the diagonal crossed product as a new associative algebra structure on ,…
Frank Hausser, Florian NillAug 4, 1997
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A Natural Basis for Spinor and Vector Fields on the Noncommutative sphere
The product of two Heisenberg-Weil algebras contains the Jordan-Schwinger representation of su(2). This Algebra is quotiented by the square-root of the Casimir to produce a non-associative algebra…
Jonathan GratusAug 4, 1997
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The Alexander polynomial and finite type 3-manifold invariants
This is a revised version (replacing an older one) with typos fixed and the introduction expanded.
Stavros Garoufalidis, Nathan HabeggerAug 2, 1997
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On quantum topology, hypergraphs and flag vectors
Each rule f that assigns a vector f(G) to an (n+1)-graph G determines a class (or property) of n-manifold invariants. An invariant v=v(M) is in this class if, for any triangulated…
Jonathan FineAug 1, 1997
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From quantum to elliptic algebras
It is shown that the elliptic algebra Aq,p(sl(2)c) at the critical level c=-2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson…
J. Avan, L. Frappat, M. Rossi et al.Jul 29, 1997
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Classification of Bicovariant Differential Calculi on the Quantum Groups SLq(n+1) and Spq(2n)
For transcendental values of q all bicovariant first order differential calculi on the coordinate Hopf algebras of the quantum groups SLq(n+1) and Spq(2n) are classified. It is shown that the…
I. Heckenberger, K. SchmuedgenJul 25, 1997
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