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Amalgamated Products of Strongly RFD $\mathrm{C}^*$-algebras arising from locally compact groups

Banff International Research Station for Mathematical Innovation and Discovery

Residual finite dimensionality is the $\mathrm{C}^*$-algebraic analogue for maximal almost periodicity and residual finiteness for groups. Just as with the analogous group-theoretic properties, there is significant interest in when residual finite dimensionality is preserved under standard constructions, in particular amalgamated free products. In general, this question is quite difficult; however the answer is known when the amalgam is finite dimensional or when the two $\mathrm{C}^*$-algebras are commutative. In moving beyond these cases, group theoretic restrictions suggest that we consider central amalgams. We generalize the commutative case to pairs of so-called ``strongly residually finite dimensional" $\mathrm{C}^*$-algebras amalgamated over a central subalgebra. Examples of strongly residually finite dimensional $\mathrm{C}^*$-algebras include group $\mathrm{C}^*$-algebras associated to virtually abelian groups, certain just-infinite groups, and Lie groups with only finite dimensional irreducible unitary representations. Though this property may seem restrictive, a recent result of Thom indicates that it is in fact necessary. This is joint work with Tatiana Shulman.

Mathematics; Functional analysis; Dynamical systems and ergodic theory

video/mp4

Author affiliation: WWU Münster

2020-04-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73890

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/