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Your search keyword '"Gaviria, Isaías David Marín"' showing total 13 results
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13 results on '"Gaviria, Isaías David Marín"'

2. Relationships Between Mutations of Brauer Configuration Algebras and Some Diophantine Equations

Author

Cañadas, Agustín Moreno, Camacho, Juan David, and Gaviria, Isaías David Marín

Subjects
Mathematics - Representation Theory
Abstract

Mutations on Brauer configurations are introduced and associated with some suitable automata in order to solve generalizations of the Chicken McNugget problem. Besides, based on marked order polytopes a new class of diophantine equations called Gelfand-Tsetlin equations are also solved. The approach allows giving an algebraic description of the schedule of an AES key via some suitable non-deterministic finite automata (NFA).

Published
2021

3. Brauer Configuration Algebras and Matrix Problems to Categorify Integer Sequences

Author

Cañadas, Agustín Moreno, Espinosa, Pedro Fernando Fernández, Gaviria, Isaías David Marín, and Rios, Gabriel Bravo

Subjects
Mathematics - Representation Theory, 16G20, 16G60, 16G30
Abstract

Bijections between invariants associated to indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated to solutions of the Kronecker problem and the four subspace problem are used to categorify integer sequences in the sense of Ringel and Fahr. Dimensions of the Brauer configuration algebras and their corresponding centers involved in the different processes are given as well.

Published
2021

4. Coxeter's Frieze Patterns Arising from Dyck Paths

Author

Cañadas, Agustín Moreno, Gaviria, Isaías David Marín, Rios, Gabriel Bravo, and Espinosa, Pedro Fernando Fernández

Subjects
Mathematics - Representation Theory, 16G20, 16G30, 16G60
Abstract

Frieze patterns are defined by objects of a category of Dyck paths, to do that, it is introduced the notion of diamond of Dynkin type An. Such diamonds constitute a tool to build integral frieze patterns.

Published
2021

9. Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras.

Author

Cañadas, Agustín Moreno, Ballester-Bolinches, Adolfo, and Gaviria, Isaías David Marín

Subjects
YANG-Baxter equation, ALGEBRA, QUANTUM computing, HOPF algebras
Abstract

Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as knot theory, Hopf algebras, quandles, Lie and Jordan (super) algebras, and quantum computing. One of the most successful techniques to obtain solutions of the YBE was given by Rump, who introduced an algebraic structure called the brace, which allows giving non-degenerate involutive set-theoretical solutions. This paper introduces Brauer configuration algebras, which, after appropriate specializations, give rise to braces associated with Thompson's group F. The dimensions of these algebras and their centers are also given. [ABSTRACT FROM AUTHOR]

Published
2023
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13. Brauer configuration algebras and Kronecker modules to categorify integer sequences.

Author

Cañadas, Agustín Moreno, Gaviria, Isaías David Marín, and Espinosa, Pedro Fernando Fernández

Subjects
*INTEGERS, *PROBLEM solving, *DIMENSIONS, *INVARIANTS (Mathematics), *MATHEMATICAL formulas
Abstract

Bijections between invariants associated with indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated with solutions of the Kronecker problem are used to categorify integer sequences in the sense of Ringel and Fahr. Dimensions of the Brauer configuration algebras and their corresponding centers involved in the different processes are also given. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

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