Strong 1-boundedness, $L^2$-Betti numbers, algebraic soficity, and graph products
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916197854871552 |
|---|---|
| author | Charlesworth, Ian de Santiago, Rolando Hayes, Ben Jekel, David Elayavalli, Srivatsav Kunnawalkam Nelson, Brent |
| author_facet | Charlesworth, Ian de Santiago, Rolando Hayes, Ben Jekel, David Elayavalli, Srivatsav Kunnawalkam Nelson, Brent |
| contents | We show that graph products of non trivial finite dimensional von Neumann algebras are strongly 1-bounded when the underlying *-algebra has vanishing first L2-Betti number. The proof uses a combination of the following two key ideas to obtain lower bounds on the Fuglede-Kadison determinant of matrix polynomials in a generating set: a notion called ''algebraic soficity'' for *-algebras allowing for the existence of Galois bounded microstates with asymptotically constant diagonals; a probabilistic construction of the authors of permutation models for graph independence over the diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19463 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong 1-boundedness, $L^2$-Betti numbers, algebraic soficity, and graph products Charlesworth, Ian de Santiago, Rolando Hayes, Ben Jekel, David Elayavalli, Srivatsav Kunnawalkam Nelson, Brent Operator Algebras Functional Analysis Group Theory Probability We show that graph products of non trivial finite dimensional von Neumann algebras are strongly 1-bounded when the underlying *-algebra has vanishing first L2-Betti number. The proof uses a combination of the following two key ideas to obtain lower bounds on the Fuglede-Kadison determinant of matrix polynomials in a generating set: a notion called ''algebraic soficity'' for *-algebras allowing for the existence of Galois bounded microstates with asymptotically constant diagonals; a probabilistic construction of the authors of permutation models for graph independence over the diagonal. |
| title | Strong 1-boundedness, $L^2$-Betti numbers, algebraic soficity, and graph products |
| topic | Operator Algebras Functional Analysis Group Theory Probability |
| url | https://arxiv.org/abs/2305.19463 |