Nets of graded 𝐶*-algebras over partially ordered sets

Grigoryan, S.; Lipacheva, E.; Sitdikov, A.

doi:10.1090/spmj/1576

Nets of graded $C^*$-algebras over partially ordered sets
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by S. A. Grigoryan, E. V. Lipacheva and A. S. Sitdikov
Translated by: the authors

St. Petersburg Math. J. 30 (2019), 901-915

DOI: https://doi.org/10.1090/spmj/1576

Published electronically: September 16, 2019

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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 algebra is graded by the first homotopy group of the partially ordered set. Inductive systems of $C^*$-algebras and their limits over maximal directed subsets are considered, as well as properties of morphisms for nets of Hilbert spaces and nets of $C^*$-algebras.

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