A5015342874- Advanced Operator Algebra Research
- Advanced Topics in Algebra
- Advanced Banach Space Theory
- Homotopy and Cohomology in Algebraic Topology
- Algebraic structures and combinatorial models
- semigroups and automata theory
- Noncommutative and Quantum Gravity Theories
- Advanced Algebra and Logic
- Neurological disorders and treatments
- Mathematical Dynamics and Fractals
- Advanced Topology and Set Theory
- Geometric and Algebraic Topology
- Cellular Automata and Applications
- Computability, Logic, AI Algorithms
- Coding theory and cryptography
- Quantum chaos and dynamical systems
- Holomorphic and Operator Theory
- Control and Stability of Dynamical Systems
- Advanced Thermodynamics and Statistical Mechanics
- Matrix Theory and Algorithms
- Control and Dynamics of Mobile Robots
- Mathematical Analysis and Transform Methods
- Pituitary Gland Disorders and Treatments
- Quantum many-body systems
- Dynamics and Control of Mechanical Systems
Universidade Federal de Santa Catarina
2016-2025
Brazilian Institute of Geography and Statistics
2021
Universidade Federal do Rio Grande do Sul
2021
Laboratoire de Mathématiques Analyse, Probabilités, Modélisation Orléans
2009
We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital, and the other not necessarily. focus on unital case describe conjugacy between Ott–Tomforde–Willis subshifts in terms of homeomorphism Stone duals suitable Boolean algebras, diagonal-preserving isomorphism algebras. For this, we realise algebra as groupoid partial skew group ring.
We want to relate the concepts of entropy and pressure that KMS states for C * -Algebras.Several different definitions are known in our days.The one we describe here is quite natural extends usual Dynamical Systems Thermodynamic Formalism Theory.It has advantage been very easy be introduced.It basically obtained from transfer operators (also called Ruelle operators).Later introduce concept as a min-max principle.Finally, consider state an equilibrium potential (in context -Algebras) show...
We review Kajiwara and Watatani's construction of a C*-algebra from an iterated function system (IFS). If the IFS satisfies finite branch condition or open set condition, we build injective homomorphism Kajiwara-Watatani algebras to Cuntz algebra, which can be thought as algebra lifted system, give description its image. Finally, if admits left inverse show that is isomorphic Exel's crossed product.
We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These characterize ultragraphs which the topological full group of an groupoid is isomorphism invariant. results extend those graph to ultragraph while providing another concrete example where a complete
We show how to recover a discrete twist over an ample Hausdorff groupoid from pair consisting of algebra and what we call quasi-Cartan subalgebra. identify precisely which twists arise in this way (namely, those that satisfy the local bisection hypothesis), prove assignment twisted Steinberg algebras such our construction are mutually inverse. algebraic pairs correspond effective groupoids principal groupoids. also indicate scope results by identifying large classes for hypothesis holds...
We prove the Effros-Hahn conjecture for groupoid algebras with coefficients in a sheaf, obtaining as consequence description of ideals skew inverse semigroup rings. also use to characterize when sheaf are von Neumann regular, primitive, semiprimitive, or simple. apply our results topological dynamics actions semigroups, describing existence dense orbits and minimality terms primitivity simplicity, respectively, associated algebra. Moreover, we usual complex algebra continuous functions...
We define the orbit morphism of partial dynamical systems and prove that an being isomorphism in category morphisms is equivalent to existence a continuous equivalence between given preserves essential stabilisers. show this diagonal-preserving corresponding crossed products when stabilisers actions are torsion-free abelian. also characterize \'etale groupoid isomorphic transformation some action. Additionally, we explore implications context semi-saturated orthogonal over free groups,...
We introduce partial group algebras with relations in a purely algebraic framework. Given and set of relations, we define an action prove that the resulting skew ring is isomorphic to associated algebra relations. Under suitable conditions - which always holds if base field demonstrate can also be described using topological action. Furthermore, show how subshift realized as Using action, describe simplicity terms underlying dynamics subshift.
Abstract First, we generalize the definition of a locally compact topology given by Paterson and Welch for sequence spaces to case where underlying are $T_{1}$ sober. We then consider certain semilattice basic open sets this on space all paths graph impose relations motivated definitions C*-algebra in order recover boundary path graph. This is done using techniques pointless topology. Finally, results topological graphs.
We describe KMS and ground states arising from a generalized gauge action on ultragraph C*-algebras. focus ultragraphs that satisfy Condition~(RFUM), so we can use the partial crossed product description of C*-algebras recently described by second author Danilo Royer. In particular, for with no sinks, generalize recent result Toke Carlsen Nadia Larsen: Given time evolution C*-algebra an ultragraph, induced function edge set, characterize in five different ways four ways. both cases include...