357 research outputs found
The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold
A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an
infinite sequence of penetrations into a neighborhood of a cone singularity, so
that the sequence of depths of maximal penetration has a limiting distribution.
The distribution function is the same for all such surfaces and is described by
a fairly simple formula.Comment: 20 page
A note on quantum structure constants
The Cartan-Maurer equations for any -group of the
series are given in a convenient form, which allows their direct computation
and clarifies their connection with the case. These equations, defining
the field strengths, are essential in the construction of -deformed gauge
theories. An explicit expression \om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l
for the -commutations of left-invariant one-forms is found, with \Z{ij}{kl}
\om^k \we \om^l \qonelim \om^j\we\om^i.Comment: 9 pp., LaTe
Generalizations of Maxwell (super)algebras by the expansion method
The Lie algebras expansion method is used to show that the Maxwell
(super)algebras and some of their generalizations can be derived in a simple
way as particular expansions of o(3,2) and osp(N|4).Comment: Discussion slightly expanded; published versio
Deformations of Multiparameter Quantum gl(N)
Multiparameter quantum gl(N) is not a rigid structure. This paper defines an
essential deformation as one that cannot be interpreted in terms of a
similarity transformation, nor as a perturbation of the parameters. All the
equivalence classes of first order essential deformations are found, as well as
a class of exact deformations. This work provides quantization of all the
classical Lie bialgebra structures (constant r-matrices) found by Belavin and
Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a
cubic root of unity, stands out.Comment: 15 pages. Plain Te
Quantum Principal Bundles and Corresponding Gauge Theories
A generalization of classical gauge theory is presented, in the framework of
a noncommutative-geometric formalism of quantum principal bundles over smooth
manifolds. Quantum counterparts of classical gauge bundles, and classical gauge
transformations, are introduced and investigated. A natural differential
calculus on quantum gauge bundles is constructed and analyzed. Kinematical and
dynamical properties of corresponding gauge theories are discussed.Comment: 28 pages, AMS-LaTe
Kappa-contraction from to
We present contraction prescription of the quantum groups: from to
. Our strategy is different then one chosen in ref. [P. Zaugg,
J. Phys. A {\bf 28} (1995) 2589]. We provide explicite prescription for
contraction of and generators of and arrive at
Hopf algebra .Comment: 3 pages, plain TEX, harvmac, to be published in the Proceedings of
the 4-th Colloqium Quantum Groups and Integrable Systems, Prague, June 1995,
Czech. J. Phys. {\bf 46} 265 (1996
Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras
A generalization of the results of Rasetti and Zanardi concerning avoiding
errors in quantum computers by using states preserved by evolution is
presented. The concept of dynamical symmetry is generalized from the level of
classical Lie algebras and groups to the level of dynamical symmetry based on
quantum Lie algebras and quantum groups (in the sense of Woronowicz). A natural
connection is proved between states preserved by representations of a quantum
group and states preserved by evolution with dynamical symmetry of the
appropriate universal enveloping algebra. Illustrative examples are discussed.Comment: 10 pages, LaTeX, 2 figures Postscrip
Quantum isometries and noncommutative spheres
We introduce and study two new examples of noncommutative spheres: the
half-liberated sphere, and the free sphere. Together with the usual sphere,
these two spheres have the property that the corresponding quantum isometry
group is "easy", in the representation theory sense. We present as well some
general comments on the axiomatization problem, and on the "untwisted" and
"non-easy" case.Comment: 16 page
Quantum E(2) groups and Lie bialgebra structures
Lie bialgebra structures on are classified. For two Lie bialgebra
structures which are not coboundaries (i.e. which are not determined by a
classical -matrix) we solve the cocycle condition, find the Lie-Poisson
brackets and obtain quantum group relations. There is one to one correspondence
between Lie bialgebra structures on and possible quantum deformations of
and .Comment: 8 pages, plain TEX, harvmac, to appear in J. Phys.
Quantum planes and quantum cylinders from Poisson homogeneous spaces
Quantum planes and a new quantum cylinder are obtained as quantization of
Poisson homogeneous spaces of two different Poisson structures on classical
Euclidean group E(2).Comment: 13 pages, plain Tex, no figure
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