Notes about math, research, and more.
LaTeX files
- appendix.tex
- part of consolidated-notes.tex
- auslander.tex
- What You would expect, just notes from the Auslander textbook
- Was created last week (Nov 24)
- big-picture.tex
- Nice; what I printed out to go over with Rufus.
- consolidated-notes.tex
- Pretty nicely done. Should be useful
- exotic-crossed-products.tex
- fibers.tex
- Merged into consolidatednotes
- group-extension-work.tex
- Important nice work here
- gwep.tex
- Some nice nots. No research that I can see – just notes
- may-13.tex
- may-20.tex
- weakly-almost-periodic.tex
- paper/paper.tex
Notes
- The /paper/paper.tex file is split into a main paper.tex
- ./lemma-1/main-1.tex
- ./lemma-1/mu.tex
- ./lemma-2/main-2.tex
Fixes
- A lemma that beings in main-1.tex is closed in either mu.tex (more likely) or main-2.tex.
Todo
- Fill in main theorem
Paper
Goal
Goal of the paper is to find \(C^\ast\text{-algebras}\) \(A\) and discrete group \(G\) which acts on \(A\) such that \(A \rtimesimes_{\ex} G = A\rtimes_{\inj} G\).
Methods
For a nuclear \(G-C^*{-algebra}\) \(A\) and a discrete group \(G\) acting on \(A\), the following commutative diagram exists:
\begin{tikzcd} (\ell^\infty(G)\otimes A)\rtimes_{\max} G \arrow[r, "(\mathlarger{*})"] \arrow[d, hookleftarrow, "\parbox{2cm}{\footnotesize Kranz-Siebenand}", "\parbox{1.2cm}{\footnotesize always\\ injective}"'] & (\ell^\infty(G,A^{**}))\rtimes_{\max} G \\ A\rtimes_{\ex} G \arrow[r, ->>, "\psi"'] & A\rtimes_{\inj} G \arrow[u, "\parbox{2cm}{\footnotesize $A$ nuclear gives\\ existance}"'] \end{tikzcd}