Ultragraph shift spaces and chaos

Uggioni, Bruno Brogni

doi:10.48550/arxiv.1902.05784

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ultragraphs (and their algebras) are generalizations of graphs (and their algebras) with applications in Symbolic Dynamics, Operator Algebras and Algebra, see for example [9,15,24,25,26,27,28,29,30,33,34,36,39,40]. The Leavitt path algebra associated to an ultragraph was defined in [32],…”

Section: Introductionmentioning

confidence: 99%

“…It is therefore interesting to extend known results of Leavitt path algebra theory to ultragraph Leavitt path algebras. Furthermore, since ultragraph Leavitt path algebras are algebraic analogues of ultragraph C*algebras, which are well studied and play a key role in the study of infinite alphabet shift spaces (see [26,27,28,29,30]), it is important to deepen the understanding of these algebras.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Irreducible and permutative representations of ultragraph Leavitt path algebras

Royer

2019

Forum Mathematicum

Self Cite

View full text Add to dashboard Cite

We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path algebras. We show that these representations can be built from branching system and characterize irreducible representations associated to perfect branching systems. Along the way we improve the characterization of faithfulness of Chen's irreducible representations.

show abstract