Operad <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mi mathvariant="normal">𝒜</mi><msup><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">C</mi></mrow></msup><mo>■</mo><mi mathvariant="normal">𝒟</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">n</mi><mi mathvariant="bold-italic">d</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/C1A5CAB3-B5DE-407c-9B8C-847732D0C613-M003.jpg"><?fx-imagestate width="28.27866554" height="4.99533367"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/C1A5CAB3-B5DE-407c-9B8C-847732D0C613-M003c.jpg"><?fx-imagestate width="28.27866554" height="4.99533367"?></graphic></alternatives></inline-formula>的Koszul性

樊馨蔓; 高兴; 张兆泰

doi:10.13471/j.cnki.acta.snus.2022A050

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Operad

𝒜 s^{L C} ■ 𝒟 e n d

的Koszul性

研究论文 | 更新时间：2023-12-08

- Operad $𝒜 s^{L C} ■ 𝒟 e n d$ 的Koszul性
- Koszulity of the operad $𝒜 s^{L C}$ ■ $𝒟 e n d$
- 中山大学学报(自然科学版)(中英文) 2023年62卷第6期页码：135-142
- 作者机构：
  
  1.兰州财经大学信息工程与人工智能学院，甘肃兰州730101
  2.兰州大学数学与统计学院，甘肃兰州 730000
  3.甘肃省数学与统计学基础学科研究中心，甘肃兰州 730070
  4.青海民族大学数学与统计学院，青海西宁 810007
  5.兰州大学萃英学院，甘肃兰州 730000
- 作者简介：
  
  FAN Xinman（fanxm@lzufe.edu.cn）
  GAO Xing（gaoxing@lzu.edu.cn）
  ZHANG Zhaotai（zhtzhang18@lzu.edu.cn）
- 基金信息：
  
  Natural Science Foundation of Gansu Province(22JR11RA138;20JR5RA249);National Natural Science Foundation of China(12071191);Funds for Innovative Fundamental Research Group Project of Gansu Province(23JRRA684)
- DOI：10.13471/j.cnki.acta.snus.2022A050
  中图分类号： O153.3
- 纸质出版日期：2023-11-25，
  
  网络出版日期：2023-08-31，
  
  收稿日期：2022-05-31，
  
  录用日期：2023-03-22
扫描看全文
樊馨蔓,高兴,张兆泰.Operad 𝒜sLC■𝒟end的Koszul性[J].中山大学学报(自然科学版),2023,62(06):135-142.

FAN Xinman,GAO Xing,ZHANG Zhaotai.Koszulity of the operad 𝒜sLC■𝒟end[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):135-142.
樊馨蔓,高兴,张兆泰.Operad 𝒜sLC■𝒟end的Koszul性[J].中山大学学报(自然科学版),2023,62(06):135-142. DOI： 10.13471/j.cnki.acta.snus.2022A050.

FAN Xinman,GAO Xing,ZHANG Zhaotai.Koszulity of the operad 𝒜sLC■𝒟end[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):135-142. DOI： 10.13471/j.cnki.acta.snus.2022A050.

Operad

𝒜 s^{L C} ■ 𝒟 e n d

的Koszul性

PDF下载

摘要

用重写系统的方法证明了operad

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095177&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095171&type=

15.66333294

2.87866688

是Koszul的，其中

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095181&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095180&type=

16.34066582

2.87866688

是结合operad

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095192&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095190&type=

4.31799984

2.45533323

的线性相容operad和叶型operad

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095203&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095186&type=

6.85799980

2.28600001

的Manin 黑方积.

Abstract

The Koszulity of the operad

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095302&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095300&type=

6.51933336

3.21733332

■

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51096213&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51096211&type=

8.04333401

2.62466669

in terms of the method of rewriting systems is proven

where

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51096205&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51096208&type=

6.51933336

3.21733332

■

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51096213&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51096211&type=

8.04333401

2.62466669

is the Manin black product of the linear compatible operad of the associative

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095157&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095156&type=

4.23333359

2.87866688

and the dendriform operad

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095169&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095168&type=

8.04333401

2.62466669

关键词

operadKoszul性线性相容operad叶型operadManin黑方积

Keywords

operadKoszulitylinear compatible operaddendriform operadManin black product

references

BAADER F， NIPKOW T， 1998. Term rewriting and all that［M］. Cambridge： Cambridge University Press.

EBRAHIMI-FARD K， GUO L， 2005. On products and duality of binary， quadratic， regular operads［J］. J Pure Appl Algebra， 200（3）： 293-317.

LODAY J L， 1993. Une version non commutative des algèbres de Lie： Les algèbres de Leibniz［J］. Ens Math， 39 ： 269-289.

LODAY J L， VALLETTE B， 2012. Algebraic operads［M］. Berlin： Springer.

ODESSKII A， SOKOLOV V， 2006. Algebraic structures connected with pairs of compatible associative algebras［J］. Int Math Res Notices， 2006： 43734.

ODESSKII A， SOKOLOV V， 2008. Pairs of compatible associative algebras， classical Yang-Baxter equation and quiver representations［J］.Commun Math Phys， 278（1）： 83-99.

STROHMAYER H， 2008. Operads of compatible structures and weighted partitions［J］. J Pure Appl Algebra， 212（11）： 2522-2534.

VALLETTE B， 2008. Manin products， Koszul duality， Loday algebras and Deligne conjecture［J］. Reine Angew Math， 620： 105-164.

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Operad 𝒜sLC■𝒟end的Koszul性

Koszulity of the operad 𝒜sLC■𝒟end

DOI：10.13471/j.cnki.acta.snus.2022A050

摘要

Abstract

关键词

Keywords

references

Operad $𝒜 s^{L C} ■ 𝒟 e n d$ 的Koszul性

Koszulity of the operad $𝒜 s^{L C}$ ■ $𝒟 e n d$