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FD Applet - an applet for Finite-Dimensional algebras

Grothendieck monoids of extriangulated categories

(joint work with S. Saito) arXiv preprint, August 2022. Link: arXiv:2208.02928

Study the Grothendieck monoid of an extriangulated category.

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 = projectively Wakamatsu tilting modules, and Wakamatsu tilting modules

IE-closed subcategories of commutative rings are torsion-free classes

arXiv preprint, April 2023. Link: arXiv:2304.03260

I proved the title

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.

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.

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.

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.

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

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.

Schur’s lemma for exact categories implies abelian

Published in J. Algebra, October 2021. Links: journal, arXiv:2002.09241

I proved the title.

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.

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).

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

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.

From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories

Published in Algebr. Represent. Theory, June 2023. Links: journal, arXiv:2201.00595

Compute the posets of wide subcats and ICE-closed subcats from the lattice of torsion classes

Image-extension-closed subcategories of module categories of hereditary algebras

(joint work with A. Sakai) Published in J. Pure Appl. Algebra, September 2023. Links: journal, arXiv:2208.13937

Study subcategories of a module category closed under images and extensions.

On the representation theoretic realization of exact categories Permalink

Based on paper: Classifying exact categories via Wakamatsu tilting

Classification of exact structures and CM-finite Gorenstein algebras Permalink

Based on paper: Classifying exact categories via Wakamatsu tilting

Classifications of exact structures and Cohen-Macaulay finite algebras Permalink

Based on paper: Classifications of exact structures and Cohen-Macaulay-finite algebras

Auslander-type correspondences for exact categories and cotilting modules Permalink

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

Talk to various area of young researchers.

Relations for Grothendieck groups and representation-finiteness Permalink

Based on paper: Relations for Grothendieck groups and representation-finiteness

Classifications of exact structures and CM-finite Iwanaga-Gorenstein algebras Permalink

Based on paper: Classifications of exact structures and Cohen-Macaulay-finite algebras

Relations for Grothendieck groups and representation-finiteness

Based on paper: Relations for Grothendieck groups and representation-finiteness