A. Toms

A simple C$^*$-algebra which is not $K_1$-injective

We exhibit a simple unital infinite-dimensional C$^*$-algebra $A$ which is not $K_1$-injective, i.e., the canonical map $ U(A)/U_0(A)\longrightarrow K_1(A)$ is not injective. This phenomenon is well known in the non-simple case. Indeed, a natural example is the generator $u$ of $\pi_4(U(2))\cong\mathbb{Z}/2$, and we us...