arXiv subjects
Publications and source records attributed to Shelley Hebert.
We introduce a general scheme of constructing smooth subalgebras of C$^*$-algebras that are closed under the smooth calculus of self-adjoint elements. We illustrate the scheme with a number of examples.
We explicitly construct Fredholm modules and spectral triples representing any element of $K$-homology groups of Hensel-Steinitz algebras.
We discuss $C^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, continuing the analysis from [Banach J. Math. Anal. 19 (2025), 32, 30 pages, arXiv:2412.00854] and in particular we describe their structure and compute the $K$-theory groups.
We discuss C$^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, that is, the tree of balls in the space of $s$-adic integers.
We discuss various aspects of noncommutative geometry of smooth subalgebras of Hensel-Steinitz algebras. In particular we study the structure of derivations and $K$-Theory of those smooth subalgebras.
We introduce and investigate some examples of C$^*$-algebras which are related to multiplication maps in the ring of $p$-adic integers. We find ideals within these algebras and use the corresponding short exact sequences to compute the $K$-Theory.