Haruhisa ENOMOTO
About me Read more
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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
portfolio
preprints
From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
arXiv preprint, January 2022. Link: arXiv:2201.00595
Compute the posets of wide subcats and ICE-closed subcats from the lattice of torsion classes Read more
Grothendieck monoids of extriangulated categories
arXiv preprint, August 2022. Link: arXiv:2208.02928
Study the Grothendieck monoid of an extriangulated category. Read more
Image-extension-closed subcategories of module categories of hereditary algebras
arXiv preprint, August 2022. Link: arXiv:2208.13937
Study subcategories of a module category closed under images and extensions. Read more
Maximal self-orthogonal modules and a new generalization of tilting modules
arXiv preprint, February 2023. Link: arXiv:2301.13498
Study maximal self-orthogonal modules, a new generalization of tilting modules = Wakamatsu-projective modules, and Wakamatsu tilting modules Read more
publications
Classifying exact categories via Wakamatsu tilting
Published in J. Algebra, September 2017. Links: journal, arXiv:1610.07589
Study the Morita type theorem for exact categories. The Ext-perpendicular category of cotilting modules are precisely exact category with progen & inj cogen & higher kernels. Read more
Classifications of exact structures and Cohen-Macaulay-finite algebras
Published in Adv. Math., September 2018. Links: journal, arXiv:1705.02163
I classify possible exact structures on a given additive category by using functor category, and give applications to CM-finite Iwanaga-Gorenstein algebras. Read more
Relations for Grothendieck groups and representation-finiteness
Published in J. Algebra, December 2019. Links: journal, arXiv:1806.07650
Rep-fin v.s. “AR seq generate relations for K_0” in exact categories. Read more
Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
Published in Comm. Algebra, January 2021. Links: journal, arXiv:2002.09205
For torsion-free classes over preprojective algebras and path algebras of Dynkin type, I classify simple objects using the root system. Read more
Classifying substructures of extriangulated categories via Serre subcategories
Published in Appl. Categ. Structures, April 2021. Links: journal, arXiv:2005.13381
Classified a possible extriangulated substructures on a given extriangulated category using functor category Read more
ICE-closed subcategories and wide τ-tilting modules
(joint work with A. Sakai)Published in Math. Z., June 2021. Links: journal, arXiv:2010.05433
Study Image-Cokernel-Extension closed subcategories of module categories using the poset of torsion classes and τ-tilting theory. Read more
Schur’s lemma for exact categories implies abelian
Published in J. Algebra, October 2021. Links: journal, arXiv:2002.09241
I proved the title. Read more
Monobrick, a uniform approach to torsion-free classes and wide subcategories
Published in Adv. Math., December 2021. Links: journal, arXiv:2005.01626
Motivated by the study of simple objects of exact categories, I proposed the notion of monobricks, which enables us to study wide subcategories and torsion-free classes simultaneously. Read more
The Jordan-Hölder property and Grothendieck monoids of exact categories
Published in Adv. Math., February 2022. Links: journal, arXiv:1908.05446
I consider when an exact category satisfies the Jordan-Hölder property, (JHP). Read more
Rigid modules and ICE-closed subcategories in quiver representations
Published in J. Algebra, March 2022. Links: journal, arXiv:2005.05536
Established a bijection between Image-Cokernel-Extension-closed (ICE-closed) subcats in mod kQ and rigid kQ-modules Read more
Intervals of s-torsion pairs in extriangulated categories with negative first extensions
(joint work with T. Adachi and M. Tsukamoto)Published in Math. Proc. Cambridge Philos. Soc., September 2022. Links: journal, arXiv:2103.09549
Unify bijections of the form “Interval poset of torsion pairs is isomorphic to the poset of torsion pairs in another subcategory” in the framework of extriangulated categories. Read more
talks
On the representation theoretic realization of exact categories Permalink
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Read moreClassification of exact structures and CM-finite Gorenstein algebras Permalink
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Read moreClassifications of exact structures and Cohen-Macaulay finite algebras Permalink
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Read moreAuslander-type correspondences for exact categories and cotilting modules Permalink
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Based on papers:
- Classifying exact categories via Wakamatsu tilting
- Classifications of exact structures and Cohen-Macaulay-finite algebras
Exact categories in the representation theory of algebras Permalink
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Talk to various area of young researchers. Read more
Relations for Grothendieck groups and representation-finiteness Permalink
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Read moreClassifications of exact structures and CM-finite Iwanaga-Gorenstein algebras Permalink
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Read moreRelations for Grothendieck groups and representation-finiteness
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Read moreRelations for Grothendieck groups and representation-finiteness Permalink
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Read moreThe Jordan-Hölder property, Grothendieck monoids and Bruhat inversions Permalink
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Read moreThe Jordan-Hölder property, Grothendieck monoids and Bruhat inversions Permalink
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Read moreThe Jordan-Hölder property and Grothendieck monoids of exact categories Permalink
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Read moreBruhat inversions in the symmetric group and torsion-free classes over a type A quiver Permalink
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Read moreBruhat inversions in the symmetric group and torsion-free classes over a type A quiver Permalink
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Read moreBruhat inversions in symmetric groups and representation theory of quivers of type A Permalink
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Talk to various area of young researchers. Read more
Relative simples for preprojective algebras via root systems Permalink
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This conference was canceled due to COVID-19. Read more
Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras Permalink
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Read moreSimple objects in torsion-free classes over preprojective algebras of Dynkin type Permalink
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Read moreMonobricks
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Read moreICE-closed subcategories and wide tau-tilting modules Permalink
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Abstract
I’ll introduce ICE-closed subcategories of an abelian length category, subcategories closed under taking Images, Cokernels and Extensions. Both torsion classes and wide subcategories of an abelian category are ICE-closed. We will see that ICE-closed subcategories are precisely torsion classes in some wide subcategories. For a finite-dimensional algebra, I’ll introduce the notion of wide τ-tilting modules, and extend Adachi-Iyama-Reiten’s bijection between support τ-tilting modules and torsion classes to a bijection between wide τ-tilting modules and ICE-closed subcategories. If time permits, I’ll talk about some results on ICE-closed subcategories over hereditary algebras and Nakayama algebras. This talk is based on a joint work with Arashi Sakai (Nagoya University).Links
Slide (without handwriting), Slide (with handwriting), Talk Video (recording) Read moreICE-closed subcategories over module categories Permalink
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Based on paper:
- Rigid modules and ICE-closed subcategories in quiver representations
- ICE-closed subcategories and wide τ-tilting modules
Computing various objects of an algebra from the poset of torsion classes Permalink
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Based on my paper and my SageMath program,
- From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
- The lattice of torsion classes in SageMath
Some classes of subcategories of module categories: classifications and the relation between them Permalink
Published:
Based on my papers
- [1] Monobrick, a uniform approach to torsion-free classes and wide subcategories
- [2] Rigid modules and ICE-closed subcategories in quiver representations
- [3] ICE-closed subcategories and wide τ-tilting modules (joint with A. Sakai)
Constructing the lattice of wide subcategories Permalink
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10-minutes flash talk, based on my paper
- From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
Exact-categorical properties of subcategories of abelian categories Permalink
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Two talks based on my papers on exact categories. Read more
The lattice of wide subcategories Permalink
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Based on my paper
- From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
From the lattice of torsion classes to wide and ICE-closed subcategories Permalink
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Based on my preprint: Read more
Combinatorics of lattices of subcategories of a module category Permalink
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Based on my preprint: Read more
The Grothendieck monoid of an extriangulated category Permalink
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Based on our preprint with S. Saito: Read more