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Finite dimensional point derivations for graph algebras. (English) Zbl 1191.47085
Summary: This paper focuses on finite-dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of a directed graph. We determine when such a derivation is inner, and describe situations that give rise to non-inner derivations. We also analyze the situation when the derivation corresponds to a multiplicative linear functional.

MSC:
47L40 Limit algebras, subalgebras of \(C^*\)-algebras
47L55 Representations of (nonselfadjoint) operator algebras
47L75 Other nonselfadjoint operator algebras
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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