/ 6月 22, 2018/ 静岡代数学セミナー

(+ := @shizuoka.ac.jp)

その場合，土日の1コマ目に遅刻する可能性があれば，事前に連絡しておいてもらった方が無難です。
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●6月22日（金）

13:30 – 14:30 谷本龍二（静岡大学）
Exponential matrices and modular representations of elementary abelian p-groups, I

14:45 – 15:45 松野仁樹（静岡大学大学院）
3-dimensional quadratic AS-regular algebras of Type EC

16:00 – 17:00 松田一徳（北見工業大学）
Castelnuovo-Mumford 正則度とh多項式の次数について, I

18:30 – 懇親会

●6月23日（土）

09:30 – 10:30 松田一徳（北見工業大学）
Castelnuovo-Mumford 正則度とh多項式の次数について, II

10:45 – 11:45 Erik Darpö（名古屋大学大学院）
d-representation-finite self-injective algebras

13:30 – 14:30 谷本龍二（静岡大学）
Exponential matrices and modular representations of elementary abelian p-groups, II

アブストラクト

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Exponential matrices and modular representations of elementary abelian p-groups
アブストラクト
In this talk, we give an introduction to exponential matrices, and describe a classification of exponential matrices
of size at most four-by-four, up to equivalence. We give a definition of an exponential matrix, as follow: Let k be
a field of an arbitrary characteristic. A square polynomial matrix A(T) in one variable T over k is said to be an
exponential matrix if A(T) satisfies A(0) = I and A(T) A(T’) = A(T + T’), where I is the identity matrix and T, T’ are
indeterminates over k. Two exponential matrices A(T) and B(T) of size n-by-n are equivalent if there exists a
regular matrix P of GL(n, k) such that P^{-1} A(T) P = B(T). Classifying exponential matrices in positive
characteristic p, up to equivalence, is related to classifying modular representations of elementary abelian p-groups,
up to equivalence.
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3-dimensional quadratic AS-regular algebras of Type EC
アブストラクト
Classification of AS-regular algebras is one of the main interests in non-commutative algebraic geometry.
Recently, a complete list of superpotentials (defining relations) of 3-dimensional AS-regular algebras
which are “Calabi-Yau” was given in Mori-Smith (the quadratic case) and Mori-Ueyama (the cubic case),
however, no complete list of defining relations of “all” 3-dimensional AS-regular algebras has not appeared in the literature.
The purpose of this research is to give a complete list of defining relations of “all” 3-dimensional “quadratic” AS-regular algebras,
to classify them up to isomorphism, and up to graded Morita equivalence in terms of their defining relations.
In this talk, we focus on the algebras of Type EC, that is, the case that the point scheme is an elliptic curve.
After finding the automorphism group of an elliptic curve, we list defining relations of 3-dimensional quadratic AS-regular algebras of Type EC.
If time permits, we discuss the classification up to isomorphism and up to graded Morita equivalence.
This talk is based on a joint work with Ayako Itaba.
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Castelnuovo-Mumford 正則度とh多項式の次数について
アブストラクト

h多項式(ヒルベルト級数を有理関数で表した際に、分子に現れる多項式) の次数に関するものです。
Cohen-Macaulay 環に対しては両者の値は一致しますが、その逆は成り立たないことが知られています。
１コマ目の講演では研究の背景を、２コマ目の講演では日比孝之氏(大阪大学)との共同研究
(arXiv:1711.02002, to appear in Math. Nachr.) に関してお話しします。
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Erik Darpö（名古屋大学）
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d-representation-finite self-injective algebras
アブストラクト
In this talk, I shall present a systematic method to construct
self-injective algebras which are d-representation-finite in the sense of
higher-dimensional Auslander–Reiten theory. Such algebras are given as
orbit algebras of the repetitive categories of algebras of finite global
dimension satisfying a certain finiteness condition for the Serre functor.
This generalises Riedtmann’s classical construction of
representation-finite self-injective algebras.

A principal component of the proof is the result that d-cluster-tilting
subcategories are, under certain conditions, preserved by Galois
coverings.
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https://wwp.shizuoka.ac.jp/asashiba/1-4/