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arXiv · 2008.05003

Infinite sum relations on universal C*-algebras

Giuliano Boava·Gilles G. de Castro
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Abstract

We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular, we can allow some infinite sum relations. We prove a universal property for the algebras we define and we show how the Cuntz algebra of infinite isometries as well as the Exel-Laca algebras can be described using infinite sum relations. Finally, we give some sufficient conditions for when a C*-algebra generated by projections and partial isometries is a universal C*-algebra using only norm relations, in case one still wants to avoid using relations with respect to the strong operator topology.

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Giuliano Boava, Gilles G. de Castro. 2020-08-11. Infinite sum relations on universal C*-algebras. https://arxiv.org/abs/2008.05003

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