## University of Sydney Algebra Seminar

# Kristin Courtney (University of Munster)

## Friday 29 March, 12-1pm, Place: Carslaw 375

## Amalgamated free products of strongly residually finite dimensional C*-algebras over central subalgebras

The completion of a complex group algebra gives a C*-algebra, which encodes information about the group, from its (unitary) representation theory and sometimes even up to its isomorphism class. Residual finite dimensionality is the C*-algebraic analogue for maximal almost periodicity or even 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 in certain nice cases, such as when the amalgam is finite dimensional. If we want to move to infinite dimensions, group theoretic restrictions strongly suggest that we consider central amalgams. And indeed, in 2014, Korchagin showed that any amalgamated product of separable commutative C*-algebras is residually finite dimensional. This was the first and, until now, the only result for infinite dimensional amalgams. We substantially generalize this to pairs of so-called "strongly residually finite dimensional" C*-algebras amalgamated over a common central subalgebra. Examples of strongly residually finite dimensional C*-algebras arising from groups include reduced C*-algebras associated to virtually abelian groups, certain just-infinite groups, and... what else? This is joint work with Tatiana Shulman.