41 research outputs found
On the structure of inhomogeneous quantum groups
We investigate inhomogeneous quantum groups G built from a quantum group H
and translations. The corresponding commutation relations contain inhomogeneous
terms. Under certain conditions (which are satisfied in our study of quantum
Poincare groups [12]) we prove that our construction has correct `size', find
the R-matrices and the analogues of Minkowski space for G.Comment: LaTeX file, 47 pages, existence of invertible coinverse assumed, will
appear in Commun. Math. Phy
Projective quantum spaces
Associated to the standard R-matrices, we introduce quantum
spheres , projective quantum spaces , and quantum
Grassmann manifolds . These algebras are shown to be
homogeneous quantum spaces of standard quantum groups and are also quantum
principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys.
157,591 (1993)).Comment: 8 page
Green Function on the q-Symmetric Space SU_q(2)/U(1)
Following the introduction of the invariant distance on the non-commutative
C-algebra of the quantum group SU_q(2), the Green function and the Kernel on
the q-homogeneous space M=SU(2)_q/U(1) are derived. A path integration is
formulated. Green function for the free massive scalar field on the
non-commutative Einstein space R^1xM is presented.Comment: Plain Latex, 19
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 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
Deformed Minkowski spaces: clasification and properties
Using general but simple covariance arguments, we classify the `quantum'
Minkowski spaces for dimensionless deformation parameters. This requires a
previous analysis of the associated Lorentz groups, which reproduces a previous
classification by Woronowicz and Zakrzewski. As a consequence of the unified
analysis presented, we give the commutation properties, the deformed (and
central) length element and the metric tensor for the different spacetime
algebras.Comment: Some comments/misprints have been added/corrected, to appear in
Journal of Physics A (1996
Reflection equations and q-Minkowski space algebras
We express the defining relations of the -deformed Minkowski space algebra
as well as that of the corresponding derivatives and differentials in the form
of reflection equations. This formulation encompasses the covariance properties
with respect the quantum Lorentz group action in a straightforward way.Comment: 10 page
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