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arXiv · 2411.19816

A New Geometric Morita Invariant for Higher Rank Graph $C^*$-algebras

Mackenzie Amann·Liam Gallagher·Rachael Norton·Efren Ruiz
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Abstract

Higher rank graphs, also known as $k$-graphs, are a $k$-dimensional generalization of directed graphs and a rich source of examples of $C^*$-algebras. In the present paper, we contribute to the geometric classification program for $k$-graph $C^*$-algebras by introducing a new move on $k$-graphs, called LiMaR-split, which is a generalization of outsplit for directed graphs. We show, under one additional assumption, that LiMaR-split preserves the $k$-graph $C^*$-algebras up to Morita equivalence.

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Mackenzie Amann, Liam Gallagher, Rachael Norton, Efren Ruiz. 2024-11-29. A New Geometric Morita Invariant for Higher Rank Graph $C^*$-algebras. https://arxiv.org/abs/2411.19816

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