Applications of normal forms for weighted Leavitt path algebras: simple rings and domains
Rings and Algebras
2017-03-03 v3 K-Theory and Homology
Abstract
Weighted Leavitt path algebras (wLpas) are a generalisation of Leavitt path algebras (with graphs of weight 1) and cover the algebras constructed by Leavitt. Using Bergman's Diamond lemma, we give normal forms for elements of a weighted Leavitt path algebra. This allows us to produce a basis for a wLpa. Using the normal form we classify the wLpas which are domains, simple and graded simple rings. For a large class of weighted Leavitt path algebras we establish a local valuation and as a consequence we prove that these algebras are prime, semiprimitive and nonsingular but contrary to Leavitt path algebras, they are not graded von Neumann regular.
Keywords
Cite
@article{arxiv.1607.05499,
title = {Applications of normal forms for weighted Leavitt path algebras: simple rings and domains},
author = {Roozbeh Hazrat and Raimund Preusser},
journal= {arXiv preprint arXiv:1607.05499},
year = {2017}
}