I give a self-contained introduction to two novel classes of nonselfadjoint operator algebras, namely the generalised analytic Toeplitz algebras
, associated with the “Fock space” of a graph
, and subalgebras of graph C*-algebras. These two topics are somewhat independent but in both cases I shall focus on fundamental techniques and problems related to classifying isomorphism types and to the recovery of underlying foundational structures, be they graphs or groupoids.
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