On *-Representations of Polynomial Algebras in Quantum Matrix Spaces of Rank 2
Tóm tắt
In this paper we study *-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 Mat2 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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