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q-deformed circularity for an unbounded operator in Hilbert space

Schôichi Ôta (2010)

Colloquium Mathematicae

The notion of strong circularity for an unbounded operator is introduced and studied. Moreover, q-deformed circularity as a q-analogue of circularity is characterized in terms of the partially isometric and the positive parts of the polar decomposition.

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...

Quantum Fibre Bundles. An Introduction

Tomasz Brzeziński (1997)

Banach Center Publications

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

Quantum homogeneous superspaces and quantum duality principle

Rita Fioresi (2015)

Banach Center Publications

We define the concept of quantum section of a line bundle of a homogeneous superspace and we employ it to define the concept of quantum homogeneous projective superspace. We also suggest a generalization of the QDP to the quantum supersetting.

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