25 citations · 146 across the 20 of their papers we have counts for
23 papers
Representation embeddings and the third Brauer--Thrall conjecture
Haruhisa Enomoto
Let be a representation-infinite finite-dimensional algebra over an algebraically closed field . We prove that for every infinite cardinal there is an indecomposable …
Magnitude of module categories and special biserial algebras
Haruhisa Enomoto
Børve, Horiatakis, and Kalck defined the magnitude of the module category of a representation-finite algebra as the sum of the entries of the inverse of the matrix of Hom dimension…
On the homological conjectures for Artin algebras
Haruhisa Enomoto, Rene Marczinzik
We prove that the Auslander--Reiten conjecture, the generalised Nakayama conjecture, the Nakayama conjecture, and each of the two Tachikawa conjectures are globally equivalent for…
Finiteness and growth of brick chain filtrations
Haruhisa Enomoto
We study Ringel's brick chain filtrations over finite-dimensional algebras: filtrations whose factors are filtered by copies of individual bricks, ordered so that morphisms from ea…
A counterexample to the periodicity conjecture for finite-dimensional algebras
Haruhisa Enomoto
The periodicity conjecture asks whether a finite-dimensional algebra is periodic whenever all its simple modules are periodic. We construct a -dimensional counterexample whose…
The Cartan determinant conjecture for representation-finite algebras
Haruhisa Enomoto
Let be a finite-dimensional representation-finite algebra over an algebraically closed field , and let be a finite-dimensional -module such that $\operatorname{End}_A…
An equidistribution conjecture for quotient-closed and submodule-closed subcategories
Haruhisa Enomoto
We study subcategories of the module category of a finite-dimensional algebra that are closed under quotients or submodules. We propose the quotient--submodule equidistribution con…
IE-closed subcategories of commutative rings are torsion-free classes
Haruhisa Enomoto
Let C be a subcategory of the category of finitely generated R-modules over a commutative noetheian ring R. We prove that, if C is closed under images and extensions (which we call…
Maximal self-orthogonal modules and a new generalization of tilting modules
Haruhisa Enomoto
We introduce a generalization of tilting modules of finite projective dimension, projectively Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ex…
Image-extension-closed subcategories of module categories of hereditary algebras
Haruhisa Enomoto, Arashi Sakai
We study IE-closed subcategories of a module category, subcategories which are closed under taking Images and Extensions. We investigate the relation between IE-closed subcategorie…
Grothendieck monoids of extriangulated categories
Haruhisa Enomoto, Shunya Saito
We study the Grothendieck monoid (a monoid version of the Grothendieck group) of an extriangulated category, and give some results which are new even for abelian categories. First,…
From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
Haruhisa Enomoto
In this paper, we compute the posets of wide subcategories and ICE-closed subcategories from the lattice of torsion classes in an abelian length category in a purely lattice-theore…
Collaboration between high schools in Japan and Argentina for cosmic-ray research using CosmicWatches
Takeshi Nakamori, Mika Takanashi, Rikako Kono +12
Cosmic rays are ubiquitous and readily available, making them a good teaching tool for particle and astrophysics by young students. Tan-Q is an inclusive outreach and educational p…
ICE-closed subcategories and wide -tilting modules
Haruhisa Enomoto, Arashi Sakai
In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of an abelian length category using torsion classes. To each interval $[\mathcal{U},\mathcal{T}…
Classifying substructures of extriangulated categories via Serre subcategories
Haruhisa Enomoto
We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar way to the aut…
Rigid modules and ICE-closed subcategories in quiver representations
Haruhisa Enomoto
We introduce image-cokernel-extension-closed (ICE-closed) subcategories of module categories. This class unifies both torsion classes and wide subcategories. We show that ICE-close…
Monobrick, a uniform approach to torsion-free classes and wide subcategories
Haruhisa Enomoto
For a length abelian category, we show that all torsion-free classes can be classified by using only the information on bricks, including non functorially-finite ones. The idea is…
Schur's lemma for exact categories implies abelian
Haruhisa Enomoto
We show that for a given exact category, there exists a bijection between semibricks (pairwise Hom-orthogonal set of bricks) and length wide subcategories (exact extension-closed l…
Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
Haruhisa Enomoto
For an element of the simply-laced Weyl group, Buan-Iyama-Reiten-Scott defined a subcategory of a module category over a preprojective algebra of Dynkin type.…
The Jordan-Hölder property and Grothendieck monoids of exact categories
Haruhisa Enomoto
We investigate the Jordan-Hölder property (JHP) in exact categories. First, we show that (JHP) holds in an exact category if and only if the Grothendieck monoid introduced by Beren…
Relations for Grothendieck groups and representation-finiteness
Haruhisa Enomoto
For an exact category , we study the Butler's condition "AR=Ex": the relation of the Grothendieck group of is generated by Auslander-Reiten conflations.…
Classifications of exact structures and Cohen-Macaulay-finite algebras
Haruhisa Enomoto
We give a classification of all exact structures on a given idempotent complete additive category. Using this, we investigate the structure of an exact category with finitely many…
Classifying exact categories via Wakamatsu tilting
Haruhisa Enomoto
Using the Morita-type embedding, we show that any exact category with enough projectives has a realization as a (pre)resolving subcategory of a module category. When the exact cate…