94 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
Covering and gluing of algebras and differential algebras
Extending work of Budzynski and Kondracki, we investigate coverings and
gluings of algebras and differential algebras. We describe in detail the gluing
of two quantum discs along their classical subspace, giving a C*-algebra
isomorphic to a certain Podles sphere, as well as the gluing of
U_{\sqrt{q}}(sl_2)-covariant differential calculi on the discs.Comment: latex2e, 27 page
A realization of the quantum Lorentz group
A realization of a deformed Lorentz algebra is considered and its irreducible
representations are found; in the limit , these are precisely the
irreducible representations of the classical Lorentz group.Comment: This a short version of the Phys.Lett.B publicatio
Dirac Operator on the Quantum Sphere
We construct a Dirac operator on the quantum sphere which is
covariant under the action of . It reduces to Watamuras' Dirac
operator on the fuzzy sphere when . We argue that our Dirac operator
may be useful in constructing invariant field theories on
following the Connes-Lott approach to noncommutative geometry.Comment: 13 page
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
On the Quantum Lorentz Group
The quantum analogues of Pauli matrices are introduced and investigated. From
these matrices and an appropriate trace over spinorial indiceswe construct a
quantum Minkowsky metric. In this framework, we show explicitely the
correspondance between the SL(2,C) and Lorentz quantum groups.Comment: 17 page
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