Graph algebras
By P. M. Hajac, M. Tobolski. 2019
180 citations recorded by the source corpus.
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that reshape such graphs without ever decreasing the number of paths of length $k$. The key two algorithms work in turns each of them ending with a graph to which the other algorithm can be applied. Finally, one arrives at a specific graph realizing the optimal bound. Herein graph algebras mean path algebras and Leavitt path algebras. For the ground field $\mathbb{C}$ of complex numbers, the latter are viewed as dense subalgebras in their universal C*-completions called graph C*-algebras.
Subfields: Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/f9192d4501f8ae30a95e96e269179313fa39aca3
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In Computational Theory and Mathematics
Citations in the corpus
- Graded Steinberg algebras and their representations (2017, methodology): “In the last decade, Leavitt path algebras [2, 5] were introduced as an algebraisation of graph C∗-algebras [36, 41] and in particular Cuntz–Krieger algebras.”
- Simplicity of algebras associated to non-Hausdorff groupoids (2018, unknown): “(2) Relations: (a) {px : x ∈ E}∪{sa : a ∈ E(1)} is a Cuntz-Krieger E-family in the sense of [24].”
- \'Etale groupoids and their $C^*$-algebras (2017, methodology): “See [33] for background on graphs in the context of graph C-algebras; we will use Raeburn’s conventions and notation for graphs throughout.”