permutative representations
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2020 ◽  
Vol 32 (2) ◽  
pp. 417-431
Author(s):  
Daniel Gonçalves ◽  
Danilo Royer

AbstractWe 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.


2020 ◽  
Vol 63 (4) ◽  
pp. 787-801
Author(s):  
Christopher Linden

AbstractRepresentations of the Cuntz algebra ${\mathcal{O}}_{N}$ are constructed from interval dynamical systems associated with slow continued fraction algorithms introduced by Giovanni Panti. Their irreducible decomposition formulas are characterized by using the modular group action on real numbers, as a generalization of results by Kawamura, Hayashi, and Lascu. Furthermore, a certain symmetry of such an interval dynamical system is interpreted as a covariant representation of the $C^{\ast }$-dynamical system of the “flip-flop” automorphism of ${\mathcal{O}}_{2}$.


2019 ◽  
Vol 82 (1) ◽  
pp. 197-236 ◽  
Author(s):  
Valeriano Aiello ◽  
Roberto Conti ◽  
Stefano Rossi

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