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arXiv · 1905.03830

Nets of graded $C^*$-algebras over partially ordered sets

S. A. Grigoryan·E. V. Lipacheva·A. S. Sitdikov
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Abstract

The paper deals with $C^*$-algebras generated by a net of Hilbert spaces over a partially ordered set. The family of those algebras constitutes a net of $C^*$-algebras over the same set. It is shown that every such an algebra is graded by the first homotopy group of the partially ordered set. We consider inductive systems of $C^*$-algebras and their limits over maximal directed subsets. We also study properties of morphisms for nets of Hilbert spaces as well as nets of $C^*$-algebras.

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BibTeXRIS

S. A. Grigoryan, E. V. Lipacheva, A. S. Sitdikov. 2019-05-09. Nets of graded $C^*$-algebras over partially ordered sets. https://arxiv.org/abs/1905.03830

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