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arXiv · 1211.4605

On *-representations of polynomial algebras in quantum matrix spaces of rank 2

Olga Bershtein
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Abstract

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).

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BibTeXRIS

Olga Bershtein. 2012-11-19. On *-representations of polynomial algebras in quantum matrix spaces of rank 2. https://arxiv.org/abs/1211.4605

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