Noncommutative point derivations for matrix function algebras

Abstract

We study a class of matrix function algebras, here denoted ${\mathcal{T}}^{+}({\mathcal{C}}_n)$. We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of ${\mathcal{T}}^{+}({\mathcal{C}}_n)$. We use point derivations and information about $n\times n$ matrices to show that every ${\mathcal{T}}^{+}({\mathcal{C}}_n)$-valued derivation on ${\mathcal{T}}^{+}({\mathcal{C}}_n)$ is inner.

11 pages, this version (3rd version) updates some notation and corrects typographical errors

References in corpus (3)

• Free Semigroupoid Algebras
• Ideal Structure in Free Semigroupoid Algebras from Directed Graphs
• Nest representations of directed graph algebras

Cited by in corpus (1)

• Finite dimensional point derivations for graph algebras