On the \(C^*\)-algebra associated with \(\text{Pol}\left( \text{Mat}_{2,2}\right)_q\) (Q2754844)
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scientific article; zbMATH DE number 1668464
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(C^*\)-algebra associated with \(\text{Pol}\left( \text{Mat}_{2,2}\right)_q\) |
scientific article; zbMATH DE number 1668464 |
Statements
4 November 2001
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Fock representation
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Wick relations
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polynomial \(q\)-algebra
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On the \(C^*\)-algebra associated with \(\text{Pol}\left( \text{Mat}_{2,2}\right)_q\) (English)
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The \(*\)-algebra \(\text{Pol}\left( \text{Mat}_{2,2}\right)_q\) is a \(q\)-analogue of the polynomial algebra on the space of complex \(2\times 2\) matrices. Let \(\mathcal A_q\) be the associated \(C^*\)-algebra. It is proved that its Fock representation is faithful, and \(\mathcal A_q\) is isometrically isomorphic to the \(C^*\)-algebra generated by the operators of the Fock representation.
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