# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 3, September 2020  pp. 201–216.

Quantum Stiefel manifolds

Authors:  Saurabh, Bipul
Author institution:IIT Gandhinagar, Palaj Gandhinagar 382 355, India

Summary:  Podkolzin and Vainerman claimed to prove that the *-algebra Sqn,m underlying SUq(n)/SUq(n-m) is the universal *-algebra given by a finite set of generators and relations. This can be used to show that C(SUq(n)/ SUq(n-m)) is the universal C*-algebra given by a finite set of generators and relations. But it appears that there is a mistake in the proof of the first claim which invalidates the latter claim. In this article, we establish in an independent way that C(SUq(n)/SUq(n-m)) can be defined by a finite set of generators and relations.