On the lack of inverses to C*-extensions related to property T groups
V. Manuilov, K. Thomsen

TL;DR
This paper investigates the invertibility properties of certain C*-extensions associated with property T groups, demonstrating non-invertibility and non-semi-invertibility through advanced algebraic techniques.
Contribution
It provides new examples and proofs showing that some C*-extensions related to property T groups are not invertible or semi-invertible, extending understanding of their algebraic structure.
Findings
A non-invertible C*-extension example is identified.
A modified example is shown to be not invertible up to homotopy.
The vanishing of a specific element in the asymptotic tensor product is demonstrated.
Abstract
Using ideas of S. Wassermann on non-exact -algebras and property T groups, we show that one of his examples of non-invertible C*-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a C*-extension which is not even invertible up to homotopy.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Mathematical Analysis and Transform Methods
