Homological Ideals as Integer Specializations of Some Brauer Configuration Algebras
Pedro Fernando Fern\'andez Espinosa, Agust\'in Moreno Ca\~nadas
TL;DR
This paper characterizes and counts homological ideals in Nakayama algebras using integer specializations of Brauer configuration algebras, linking the enumeration to Fibonacci number categorification.
Contribution
It introduces a novel approach connecting homological ideals in Nakayama algebras with Brauer configuration algebras and Fibonacci number categorification.
Findings
Homological ideals are characterized and enumerated via integer specializations.
The enumeration relates to the categorification of Fibonacci numbers.
A new connection between algebraic structures and Fibonacci categorification is established.
Abstract
In this paper homological ideals associated to some Nakayama algebras are characterized and enumerated via integer specializations of some suitable Brauer configuration algebras. Besides, it is shown how the number of such homological ideals can be connected with the categorification process of Fibonacci numbers defined by Ringel and Fahr.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications