Equivalences of derived categories of algebras and Lie algebras realized by Ringel-Hall algebras of algebras

代数派生范畴与代数的林格尔-霍尔代数实现的李代数的等价

• 批准号: 21540036
• 负责人: ASASHIBA Hideto
• 金额: $ 2.83万
• 依托单位: Shizuoka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540036/
• 关键词: 多元環; 導来圏; グロタンディーク構成; 被覆; ラックス関手; ホール代数; 導来同値; 2圏; 反復圏; 軌道圏; スマッシュ積; 群作用; 次数付き圏

Let k be a commutative ring, I a small category and denote by k-Cat the 2-category of small k-categories. For 2-categories B, C, denote by Colax(B,C) the 2-category consisting of the colax functors from B to C and the lax transformations between them. We proved that each pseudofuncor C→D of 2-categories induces a pseudofunctor Colax(B,C)→Colax(B,D) for all 2-categories B, and defined the "module category", the "derived category", and derived equivalences of colax functors I→k-Cat by using it. We proved that if two such colax functors are derived equivalent, then so are their Grothendieck constructions, by which we gave a way to glue derived equivalences together.

设k是交换环，i是小范畴，k-Cat表示小k-范畴的2-范畴。对于2-范畴B，C，用Colax(B，C)表示由从B到C的Colax函子和它们之间的Lax变换组成的2-范畴。证明了2-范畴的每个伪函子C→D对所有2-范畴B都诱导出一个伪函子Colax(B，C)→Colax(B，D)，并利用它定义了Colax函子I→k-Cat的“模范畴”、“派生范畴”及其导出等价.我们证明了如果两个这样的Colax函子是导出等价的，那么它们的Grothendieck结构也是导出等价的，由此我们给出了一种将导出等价粘合在一起的方法。

项目成果

Derived equivalences and Grothendieck constructions of lax functors from a small category to the 2-category of k-linear categories

松散函子从小范畴到 k 线性范畴的 2 范畴的推导等价和 Grothendieck 构造

• 发表时间: 2010
• 作者: Masanori Kobayashi;et al;Terai Naoki and Trung Ngo Viet;Hideto Asashiba;T. Ashikaga and K.-I. Yoshikawa;西田憲司;Ogata Shoetsu;M. Kobayashi and S. Odagiri;浅芝秀人
• 通讯作者: 浅芝秀人

Derived equivalence classification of generalized multifold extensions of piecewise hereditary algebras of tree type

树型分段遗传代数广义多重扩张的导出等价分类

• 发表时间: 2015
• 期刊: Algebra and Discrete Mathematics Jounal
• 作者: Asashiba;Hideto;浅芝 秀人，木村真弓
• 通讯作者: 浅芝 秀人，木村真弓

Quantum ruled surfaces defined by quivers

由颤动定义的量子统治表面

• 发表时间: 2009
• 期刊: 第54回代数学シンポジューム報告集
• 作者: 漆原宏次;白井聡;天野諭;松元千陽;鈴木雄大;Urushihara & Miller;佐藤眞久;Izuru Mori
• 通讯作者: Izuru Mori

「論説」多元環の導来同値分類

《社论》多维代数的导出等价分类

• 发表时间: 2012
• 期刊: 日本数学会「数学」
• 作者: Hideto Asashiba; Mayumi Kimura;Hideto Asashiba;Hideto Asashiba;Izuru Mori and Kenta Ueyama;浅芝 秀人;浅芝 秀人，木村 真弓;Hideto Asashiba
• 通讯作者: Hideto Asashiba

Derived equiva-lences and Grothendieck constructions of lax functors

松散函子的导出等价和格洛腾迪克构造

• 发表时间: 2011
• 作者: Y.Mizusawa;T.Itoh;M.Ozaki;Akira Ishii;Hideto Asashiba
• 通讯作者: Hideto Asashiba