arXiv:1410.1835math.RA
Leavitt path algebras: the first decade
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Abstract
The algebraic structures known as {\it 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 algebras to the general mathematical community; to present some of the important results in the subject; and to describe some of the field's currently unresolved questions.
Graph theory offers one nice illustration of the transpose (for square matrices). Here's a directed graph: ⬐---------¬ n₁ → n₂ → n₃ It can be represented by this adjacency matrix: X = [ 0 1 0 ] [ 0 0 1 ] [ 1 0 0 ] See how there is a 1 for each row i and column j where there is…
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