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

Abstract

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 AV generated by an n-tuple of U-twisted isometries V with respect to a fixed n 2 -tuple U = {Ui j : 1 ≤ i < j ≤ n} of commuting unitaries (see [14]). Identifying any point of the joint spectrum σ (U) of the commutative C∗-algebra generated by ({Ui j : 1 ≤ i < j ≤ n}) with a skew-symmetric matrix, we show that the algebra AV is K-stable under the assumption that σ (U) does not contain any degenerate, skew-symmetric matrix. Finally, we prove the same result for the C∗-algebra generated by a tuple of free U-twisted isometries.