Algebra Seminar: Courtney -- Amalgamated free products of strongly residually finite dimensional C*-algebras over central subalgebras

Kristin Courtney (University of Munster) 

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

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

Abstract: 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.