arXiv subjects

İsmail Alperen Öğüt

Publications and source records attributed to İsmail Alperen Öğüt.

5 recordsLinked to original sources

arXiv2026

Conclusive Posets and Torsion in First Homology

We show that a finite poset is conclusive in the sense of Cigler, Jerman and Wojciechowski if and only if the first integral homology group of its order complex is either zero or has positive free rank. Building on the poset splitting machinery developed by Cianci and Ottina, we show that posets on $13$ elements with four maximal and four minimal elements do not admit torsion in the first homology, which was the only remaining configuration whose torsion behavior was unknown. Consequently, we obtain that the only inconclusive posets on $13$ elements are the two dual minimal finite models of the real projective plane. We also provide a rank criterion for the vanishing of the first cohomology over a field.

math.CO↗

arXiv2026

Homomorphism extension problem for subdirect products of finite groups

Motivated by the simplification of decomposition formulas for fibred bisets, we study the homomorphism extension problem for subdirect products of finite groups when the codomain is an abelian group satisfying certain hypothesis. We prove that every homomorphism of subdirect products whose Goursat quotients have trivial Schur multipliers is extensible. We also examine the case where subdirect products contain a twisted diagonal subgroup and investigate the functoriality of the extensibility property.

math.GR↗

arXiv2021

Some deformations of the fibred biset category

We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are given by simpler formulas. Those larger categories are constructed from a partial category of subcharacters by linearizing and introducing a cocycle.

math.RT↗

arXiv2021

Semisimplicity of the deformations of the subcharacter algebra of an abelian group

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of certain simple modules of the deformations of the subcharacter algebra of a finite group. For finite abelian groups, we prove that the deformation given by the inclusion of the natural numbers, which corresponds to the algebra generated by the fibred bisets over a field of characteristic zero, is not semisimple. In the cyclic group of prime order case, we provide a complete description of the semisimple deformations.

math.RT↗

arXiv2020

Semisimplicity of some deformations of the subgroup category and the biset category

We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star product. For some deformations of the subgroup category, too, we prove a semisimplicity property. The method is to embed the deformations of the biset category into the more easily described deformations of the subgroup group category.

math.RT↗