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Tomasz Brzezinski

Publications and source records attributed to Tomasz Brzezinski.

61 records · Page 4Linked to original sources
arXiv1996

Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are in bijective correspondence with equivariant maps $V\to P$, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with $\ad$-covariant maps $A\to P$.

hep-th↗
arXiv1995

Quantum Homogeneous Spaces as Quantum Quotient Spaces

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail.

q-alg↗
arXiv1995

Representation-theoretic derivation of the Temperley-Lieb-Martin algebras

Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.

hep-th↗
arXiv1994

Dynamical r-matrices and Separation of Variables: The Generalised Calogero-Moser Model

A generalisation of the classical Calogero-Moser model obtained by coupling it to the Gaudin model is considered. The recently found classical dynamical r-matrix [E. Billey, J. Avan and O. Babelon, PAR LPTHE 93-55] for the Euler-Calogero-Moser model is used to separate variables for this generalised Calogero-Moser model in the case in which there are two Calogero-Moser particles. The model is then canonically quantised and the same classical r-matrix is employed to separate variables in the Schrödinger equations.

hep-th↗
arXiv1993

Quantum group gauge theory on quantum spaces

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces).

hep-th↗
arXiv1992

A Class of Bicovariant Differential Calculi on Hopf Algebras

We introduce a large class of bicovariant differential calculi on any quantum group $A$, associated to $Ad$-invariant elements. For example, the deformed trace element on $SL_q(2)$ recovers Woronowicz' $4D_\pm$ calculus. More generally, we obtain a sequence of differential calculi on each quantum group $A(R)$, based on the theory of the corresponding braided groups $B(R)$. Here $R$ is any regular solution of the QYBE.

hep-th↗