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Noncommutative point derivations for matrix function algebras

Benton L. Duncan
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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.

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Benton L. Duncan. 2006-08-22. Noncommutative point derivations for matrix function algebras. https://arxiv.org/abs/math/0503643

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