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On *-Representations of Polynomial Algebras in Quantum Matrix Spaces of Rank 2 by Bershtein, Olga is a scholarly article available to read on EtoBox.

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In this paper we study of *-representations for polynomial algebras on quantum matrix spaces. We deal with two special cases of the polynomial algebras, namely the algebra of polynomials on quantum complex matrices $\mathrm{Mat_2}$ and on quantum complex symmetric matrices $\mathrm{Mat_2^{sym}}$. For the second algebra we classify all irreducible *-representations by bounded operators in a Hilbert space (up to a unitary equivalence). Moreover, we present a construction of *-representations of the above algebras which enables to obtain the full list of *-representations (sometimes by passing to subrepresentations).

Author

Bershtein, Olga

Published

2012

Language

EN