Leavitt path algebras: the first decade

@article{Abrams2014LeavittPA,
  title={Leavitt path algebras: the first decade},
  author={G. Abrams},
  journal={Bulletin of Mathematical Sciences},
  year={2014},
  volume={5},
  pages={59-120}
}
  • G. Abrams
  • Published 2014
  • Mathematics
  • Bulletin of Mathematical Sciences
The algebraic structures known as Leavitt path algebras were initially developed in 2004 by Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the author and Aranda Pino. During the intervening decade, these algebras have attracted significant interest and attention, not only from ring theorists, but from analysts working in C∗-algebras, group theorists, and symbolic dynamicists as well. The goal of this article is threefold: to introduce the notion of Leavitt path… Expand
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TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS
Let E be any directed graph, and K be any field. For any ideal I of the Leavitt path algebra LK(E) we provide an explicit description of a set of generators for I. This description allows us toExpand
The classification question for Leavitt path algebras
We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between ${\mathbb Z}$-graded algebras. As ourExpand
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