arXiv subjects

Malgorzata Rowicka-Kudlicka

Publications and source records attributed to Malgorzata Rowicka-Kudlicka.

4 recordsLinked to original sources

arXiv2001

Exponential equations for the quantum "az+b" group

We consider quantum group theory on the Hilbert space level. We find all solutions for scalar and general exponential equations for the quantum ``az+b'' group. It turns out that there is a simple formula for all of them involving the quantum exponential function F_N. The very interesting theorem we prove by the way is the one on the existence of normal extension of certain sum of normal operators. To put it differently, we find all unitary representations of the braided quantum group related to the quantum ``az+b'' group. This is the most difficult result needed to classify all unitary representations of the quantum ``az+b'' group. Eventually this enables us to give a formula for all unitary representations of the quantum ``ax+b'' group in our next paper.

math.QA↗

arXiv2001

Unitary representations of the quantum "ax+b" group

We find all unitary representations of the quantum "ax+b" group. It turns out that this quantum group is selfdual in the sense that all unitary representations are 'numbered' by elements of the same group. Moreover, we discover the formula for all unitary representations involving S.L. Woronowicz's quantum exponential function.

math.QA↗

arXiv2001

An example of a braided category of C*- algebras

A braided category of C*-algebras is constructed. Its objects are C*-algebras endowed with an action of the group R, its morphisms are C*-algebras morphisms intertwining the action of R, the crossed product of its two objects essentially depends on the action of R on considered C*-algebras. Crossed products of any object with the algebra of all continuous vanishing at infinity functions on R and algebras of all continuous functions on one- and twodimensional tori are discussed.

q-alg↗

arXiv2001

Braided quantum groups related to the quantum "ax+b" group

We consider quantum group theory on the Hilbert space level. We find all unitary representations of three braided quantum groups related to the quantum ``ax+b'' group. First we introduce an auxiliary braided quantum group, which is apparently not related to the quantum ``ax+b'' group, but easy to work with. We find all unitary representations of this quantum group. Then we use this result to find all unitary representations of another braided quantum group, whose C*-algebra is generated by two (out of three) generators generating (in the sense of Woronowicz) C*-algebra of the quantum ``ax+b''- group. We find all unitary representations of this other braided quantum group. This is the most difficult result needed to classify all unitary representations of the quantum ``ax+b'' group.

math.QA↗