59 research outputs found
Quantum Minkowski spaces
A survey of results on quantum Poincare groups and quantum Minkowski spaces
is presented.Comment: one reference added, 13 pages, LaTeX fil
On representation theory of quantum groups at roots of unity
Irreducible representations of quantum groups (in Woronowicz'
approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of
being an~odd root of unity. Here we find the~irreducible representations
for all roots of unity (also of an~even degree), as well as describe
"the~diagonal part" of tensor product of any two irreducible representations.
An~example of not completely reducible representation is given. Non--existence
of Haar functional is proved. The~corresponding representations of universal
enveloping algebras of Jimbo and Lusztig are provided. We also recall the~case
of general~. Our computations are done in explicit way.Comment: 31 pages, Section 2.7 added and other minor change
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
q-deformed Dirac Monopole With Arbitrary Charge
We construct the deformed Dirac monopole on the quantum sphere for arbitrary
charge using two different methods and show that it is a quantum principal
bundle in the sense of Brzezinski and Majid. We also give a connection and
calculate the analog of its Chern number by integrating the curvature over
.Comment: Technical modifications made on the definition of the base. A more
geometrical trivialization is used in section
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
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
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
Induced representations of quantum kinematical algebras
We construct the induced representations of the null-plane quantum Poincar\'e
and quantum kappa Galilei algebras in (1+1) dimensions. The induction procedure
makes use of the concept of module and is based on the existence of a pair of
Hopf algebras with a nondegenerate pairing and dual bases.Comment: 8 pages,LaTeX2e, to be published in the Proceedings of XXIII
International Colloquium on Group-Theoretical Methods in Physics, Dubna
(Russia), 31.07--05.08, 200
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