K-stability of C∗-algebras generated by isometries and unitaries with twisted commutation relations

In this article, we define a family of C∗-algebras that are generated by a finite set of unitaries and isometries satisfying certain twisted commutation relations and prove their K-stability. This family includes the C∗-algebra of doubly non-commuting isometries and free twist of isometries. Next, we consider the C∗-algebra generated by an n-tuple of -twisted isometries with respect to a fixed n2-tuple of commuting unitaries (see [14]). Identifying any point of the joint spectrum of the commutative C∗-algebra generated by ({Uij:1≤i<j≤n}) with a skew-symmetric matrix, we show that the algebra is K-stable under the assumption that does not contain any degenerate, skew-symmetric matrix. Finally, we prove the same result for the C∗-algebra generated by a tuple of free -twisted isometries.