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23 April 2024

» arxiv » 1507.1247

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The Cuntz splice does not preserve $*$-isomorphism of Leavitt path algebras over $mathbb{Z}$
Rune Johansen ; Adam P. W. Sørensen ;
Date:	5 Jul 2015
Abstract:	We show that the Leavitt path algebras $L_{2,mathbb{Z}}$ and $L_{2-,mathbb{Z}}$ are not isomorphic as $*$-algebras. There are two key ingredients in the proof. One is a partial algebraic translation of Matsumoto and Matui’s result on diagonal preserving isomorphisms of Cuntz--Krieger algebras. The other is a complete description of the projections in $L_{2,mathbb{Z}}$ based on a similar description of the unitaries in $L_{2,mathbb{Z}}$ given by Brownlowe and the second named author.
Source:	arXiv, 1507.1247
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