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Osamu Iyama

  1. Preprojective algebras and c-sortable words.

    Tue, 02/23/2010 - 16:01 — SomNambul
    Authors: Osamu Iyama, Claire Amiot, Idun Reiten, Gordana Todorov
    Subjects: Representation Theory
    Abstract

    Let $Q$ be an acyclic quiver and $\Lambda$ be the completion of the
    preprojective algebra of $Q$ over an algebraically closed field $k$. To any
    element $w$ in the Coxeter group of $Q$, Buan, Iyama, Reiten and Scott have
    introduced and studied in \cite{Bua2} a finite dimensional algebra
    $\Lambda_w=\Lambda/I_w$. In this paper we look at filtrations of $\Lambda_w$
    associated to any reduced expression $\ww$ of $w$. We are specially interested
    in the case where the word $\ww$ is $c$-sortable where $c$ is a Coxeter
    element.

  2. 2-Auslander algebras associated with reduced words in Coxeter groups.

    Thu, 02/18/2010 - 16:01 — SomNambul
    Authors: Osamu Iyama, Idun Reiten
    Subjects: Representation Theory
    Abstract

    In this paper we investigate the endomorphism algebras of standard cluster
    tilting objects in the stably 2-Calabi-Yau categories $\Sub{\Lambda_w}$ with
    elements $w$ in Coxeter groups in \cite{BIRSc}. They are examples of the
    2-Auslander algebras introduced in \cite{I1}. Generalizing work in \cite{GLS1}
    we show that they are quasihereditary, even strongly quasihereditary in the
    sense of \cite{R}.

  3. Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2.

    Wed, 01/13/2010 - 16:01 — SomNambul
    Authors: Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi, Rei Inoue
    Subjects: Quantum Algebra
    Abstract

    We prove the periodicities of the restricted T and Y-systems associated with
    the quantum affine algebra of type C_r, F_4, and G_2 at any level. We also
    prove the dilogarithm identities for these Y-systems at any level. Our proof is
    based on the tropical Y-systems and the categorification of the cluster algebra
    associated with any skew-symmetric matrix by Plamondon.

  4. Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r.

    Wed, 01/13/2010 - 16:01 — SomNambul
    Authors: Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi, Rei Inoue
    Subjects: Quantum Algebra
    Abstract

    We prove the periodicities of the restricted T and Y-systems associated with
    the quantum affine algebra of type B_r at any level. We also prove the
    dilogarithm identities for the Y-systems of type B_r at any level. Our proof is
    based on the tropical Y-systems and the categorification of the cluster algebra
    associated with any skew-symmetric matrix by Plamondon. Using this new method,
    we also give an alternative and simplified proof of the periodicities of the T
    and Y-systems associated with pairs of simply laced Dynkin diagrams.

  5. Recollement of homotopy categories and Cohen-Macaulay modules.

    Tue, 11/03/2009 - 16:01 — SomNambul
    Authors: Osamu Iyama, Kiriko Kato, Jun-ichi Miyachi
    Subjects: Rings and Algebras
    Abstract

    We study the homotopy category of unbounded complexes with bounded homologies
    and its quotient category by the homotopy category of bounded complexes. We
    show the existence of a recollement of the above quotient category and it has
    the homotopy category of acyclic complxes as a triangulated subcategory. In the
    case of the homotopy category of finitely generated projective modules over an
    Iwanaga-Gorenstein ring, we show that the above quotient category are triangle
    equivalent to the stable module category of Cohen-Macaulay
    $\opn{T}_2(R)$-modules.

  6. n-representation-finite algebras and n-APR tilting.

    Fri, 09/04/2009 - 12:10 — SomNambul
    Authors: Osamu Iyama, Steffen Oppermann
    Subjects: Representation Theory
    Abstract

    We introduce the notion of n-representation-finiteness, generalizing
    representation-finite hereditary algebras. We establish the procedure of n-APR
    tilting, and show that it preserves n-representation-finiteness. We give some
    combinatorial description of this procedure, and use this to completely
    describe a class of n-representation-finite algebras called ``type A''.

  7. n-representation-finite algebras and fractionally Calabi-Yau algebras.

    Wed, 08/26/2009 - 14:58 — SomNambul
    Authors: Martin Herschend, Osamu Iyama
    Subjects: Representation Theory
    Abstract

    In this short paper, we study $n$-representation-finite algebras from the
    viewpoint of fractionally Calabi-Yau algebras. We shall show that all
    $n$-representation-finite algebras are twisted fractionally Calabi-Yau. We also
    show that twisted $\frac{n(\ell-1)}{\ell}$-Calabi-Yau algebras of global
    dimension $n$ are $n$-representation-finite for any $\ell>0$. As an
    application, we give a construction of $n$-representation-finite algebras using
    the tensor product.

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