Updated on 2022/03/25

写真a

 
NAKAOKA Hiroyuki
 
Organization
Graduate School of Mathematics Division of Mathematics Fundamental Mathematics Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Associate professor

Degree 1

  1. 博士(数理科学) ( 2009.3   東京大学 ) 

 

Papers 3

  1. n-Exangulated categories (II): Constructions from n-cluster tilting subcategories

    Herschend M., Liu Y., Nakaoka H.

    Journal of Algebra   Vol. 594   page: 636 - 684   2022.3

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    Language:Japanese   Publisher:Journal of Algebra  

    In n-Exangulated Categories (I), we introduced the notion of n-exangulated categories for each positive integer n. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a common generalization of n-exact categories in the sense of Jasso and (n+2)-angulated categories in the sense of Geiss-Keller-Oppermann. In this second article we introduce the notion of n-cluster tilting subcategories for extriangulated categories with enough projectives and injectives and show that under certain conditions such n-cluster tilting subcategories are n-exangulated.

    DOI: 10.1016/j.jalgebra.2021.11.042

    Scopus

  2. Finite gentle repetitions of gentle algebras and their Avella-Alaminos-Geiss invariants

    Nakaoka Hiroyuki

    COMMUNICATIONS IN ALGEBRA     2021.11

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    Language:Japanese   Publisher:Communications in Algebra  

    Among finite dimensional algebras over a field K, the class of gentle algebras is known to be closed by derived equivalences. Although a classification up to derived equivalences is usually a difficult problem, Avella-Alaminos and Geiss have introduced derived invariants for gentle algebras A, which can be calculated combinatorially from their bound quivers, applicable to such classification. Ladkani has given a formula to describe the dimensions of the Hochschild cohomologies of A in terms of some values of its Avella-Alaminos–Geiss invariants. This in turn implies a cohomological meaning of these values. Since most of the other values do not appear in this formula, it will be a natural question to ask if there is a similar cohomological meaning for such values. In this article, we construct a sequence of gentle algebras (Formula presented.) indexed by positive integers by a procedure which we call finite gentle repetitions, in order to relate these values of Avella-Alaminos–Geiss invariants of A to the dimensions of Hochschild cohomologies of (Formula presented.) On the way we will see that the Avella-Alaminos–Geiss invariants of (Formula presented.) are completely determined by those of A. Therefore one may expect that the finite gentle repetitions would preserve derived equivalences in a nice situation. In the last part of this article, we will see how the generalized Auslander–Platzeck–Reiten reflection can be related to the finite gentle repetition.

    DOI: 10.1080/00927872.2021.2008412

    Web of Science

    Scopus

  3. n-exangulated categories (I): Definitions and fundamental properties

    Herschend Martin, Liu Yu, Nakaoka Hiroyuki

    JOURNAL OF ALGEBRA   Vol. 570   page: 531 - 586   2021.3

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    Publisher:Journal of Algebra  

    DOI: 10.1016/j.jalgebra.2020.11.017

    Web of Science

    Scopus

KAKENHI (Grants-in-Aid for Scientific Research) 1

  1. Theoretical development of homological algebra in exact categories and triangulated categories

    Grant number:17K18727  2017.6 - 2020.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Challenging Research (Exploratory)

    Nakaoka Hiroyuki

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    Authorship:Principal investigator 

    Grant amount:\3900000 ( Direct Cost: \3000000 、 Indirect Cost:\900000 )

    The collaboration with Yann Palu, in which we have introduced the notion of an extriangulated category, was published after revision. In the sequel, a collaboration with Yu Liu on the heart of cotorsion pairs on extriangulated categories was published after revision.
    In collaboration with Martin Herschend and Yu Liu, we have introduced the notion of an n-exangulated category as a higher version of extriangulated category. This manuscript was submitted to a journal, now under review. In collaboration with Osamu Iyama and Yann Palu, we wrote a preprint on the Auslander-Reiten theory in extriangulated categories.
    In addition, I have submitted a preprint concerning derived invariants of gentle algebras to arXiv.