# A noncommutative 2-sphere generated by the quantum complex plane

Banach Center Publications (2012)

- Volume: 98, Issue: 1, page 55-66
- ISSN: 0137-6934

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topIsmael Cohen, and Elmar Wagner. "A noncommutative 2-sphere generated by the quantum complex plane." Banach Center Publications 98.1 (2012): 55-66. <http://eudml.org/doc/282501>.

@article{IsmaelCohen2012,

abstract = {S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions on the quantum complex plane vanishing at infinity, and its unitization will be viewed as the algebra of continuous functions on a quantum 2-sphere.},

author = {Ismael Cohen, Elmar Wagner},

journal = {Banach Center Publications},

keywords = {-algebra; unbounded elements; quantum plane; quantum sphere},

language = {eng},

number = {1},

pages = {55-66},

title = {A noncommutative 2-sphere generated by the quantum complex plane},

url = {http://eudml.org/doc/282501},

volume = {98},

year = {2012},

}

TY - JOUR

AU - Ismael Cohen

AU - Elmar Wagner

TI - A noncommutative 2-sphere generated by the quantum complex plane

JO - Banach Center Publications

PY - 2012

VL - 98

IS - 1

SP - 55

EP - 66

AB - S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions on the quantum complex plane vanishing at infinity, and its unitization will be viewed as the algebra of continuous functions on a quantum 2-sphere.

LA - eng

KW - -algebra; unbounded elements; quantum plane; quantum sphere

UR - http://eudml.org/doc/282501

ER -

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