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arXiv · 1902.08719

Leavitt path algebras of hypergraphs

Raimund Preusser
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Abstract

We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of finitely separated graphs and Leavitt path algebras of row-finite vertex-weighted graphs. We find linear bases for those algebras, compute their Gelfand-Kirillov dimension, obtain some results on ring-theoretic properties like simplicity, von Neumann regularity and Noetherianess and investigate their K-theory and graded K-theory. By doing so we obtain new results on the Gelfand-Kirillov dimension and graded K-theory of Leavitt path algebras of separated graphs and on the graded K-theory of weighted Leavitt path algebras.

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Raimund Preusser. 2019-02-23. Leavitt path algebras of hypergraphs. https://arxiv.org/abs/1902.08719

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