Department of Mathematics,
University of California San Diego
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Math 243: Seminar in Functional Analysis
Patrick Hiatt
UCSD
A class of freely complemented MASAs in $L\mathbb{F}_n$
Abstract:
I will present some recent joint work with Nick Boschert and Ethan Davis where we prove that if $A_1, A_2, \dots, A_n$ are abelian tracial W$^*$-algebras for $2\leq n \leq \infty$ and $M = A_1 * \cdots * A_n$ is their free product, then any subalgebra $\mathcal{A} \subset M$ of the form $\A = \sum_{i=1}^n u_i A_i p_i u_i^*$, for some projections $p_i \in A_i$ and unitaries $u_i \in \mathcal{U}(M)$, for $1 \leq i \leq n$, such that $\sum_i u_i p_i u_i^* = 1$, is freely complemented (FC) in $M$. We also show that any of the known maximal amenable MASAs $A\subset L\mathbb{F}_n$ satisfy Popa's weak FC conjecture, namely there exists a Haar unitary in $L\mathbb{F}_n$ that's free independent to $A$.
Sri Kunnawalkam Elayavalli
December 3, 2024
11:00 AM
APM B412
Research Areas
Functional Analysis / Operator Theory****************************
