Invariance of C*‐Algebraic Properties Under a Twisted Product

ABSTRACT

In this paper, we investigate the structure of a twisted C*‐algebra , built on a unital C*‐algebra using a central projection and a unitary . The operations are defined as and . A key insight we uncover is that this twisted setup is ‐isomorphic to the direct sum . Building on that isomorphism, we offer detailed descriptions of central objects in the twisted algebra—like projections, unitaries, positive elements, and partial isometries—expressed back in terms of the underlying . Beyond that, we show how this twisting preserves a host of core C*‐algebra features and invariants. In particular, mirrors in aspects such as stable finiteness, real and stable ranks, the makeup of traces and quasitraces, the AF condition, nuclearity, exactness, nuclear dimension, and inner quasidiagonality. We also spell out how inner automorphisms act here, and we examine what happens when you stabilize the algebra or take ultrapowers. Taken together, these findings highlight how the twisted version holds onto the vital structural and regularity traits of the original.