Maximum modulus principle for “holomorphic functions” on the quantum matrix ball

摘要

We describe the Shilov boundary ideal for a q-analog of the algebra ofholomorphic functions on the unit ball in the space of $nimes n$ matrices andshow that its $C^*$-envelope is isomorphic to the $C^*$-algebra of continuousfunctions on the quantum unitary group $U_q(n)$.