01/11/2019, 14:00 in MAP/0G/017
Courtney, Kristin (Universität Münster)
Residual finite dimensionality is the C*-algebraic analogue for 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 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” C*-algebras amalgamated over a central subalgebra. Examples of strongly residually finite dimensional C*-algebras include group 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.