arXiv subjects

Menevşe Eryüzlü Paulovicks

Publications and source records attributed to Menevşe Eryüzlü Paulovicks.

2 recordsLinked to original sources

arXiv2026

$k$-graph algebras are iterated Cuntz-Pimsner algebras -- from the bottom up

We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our process, on the other hand, starts at the bottom, with Pimsner's theorem for graph algebras, and iterates upward. We actually work with product systems over $\mathbb N^k$, and the result for $k$-graphs is a special case. Our iteration step involves a ``decategorization'' of a recent theorem showing that the Cuntz-Pimsner construction is functorial at the level of ``enchilada categories''.

math.OA↗

arXiv2024

Exactness of the Cuntz-Pimsner Construction

In prior work we described how the Cuntz-Pimsner construction may be viewed as a functor. The domain of this functor is a category whose objects are $C^*$-correspondences and morphisms are isomorphism classes of certain pairs comprised of a $C^*$-correspondence and an isomorphism. The codomain is the well-studied category whose objects are $C^*$-algebras and morphisms are isomorphism classes of $C^*$-correspondences. In this paper we show that certain fundamental results in the theory of Cuntz-Pimsner algebras are direct consequences of the functoriality of the Cuntz-Pimsner construction. In addition, we describe exact sequences in the target and domain categories, and prove that the Cuntz-Pimsner functor is exact.

math.OA↗