The
shifted Poisson structure on derived representation schemes of Koszul Calabi-Yau
algebras

doi:10. 13471/j.cnki.acta.snus.2020.03.04.2020A009

Acta Scientiarum Naturalium Universitatis Sunyatseni ›› 2020, Vol. 59 ›› Issue (5): 1-18.doi: 10. 13471/j.cnki.acta.snus.2020.03.04.2020A009

The shifted Poisson structure on derived representation schemes of Koszul Calabi-Yau algebras

CHEN Xiaojun¹，CHEN Youming ²，Alimjon ESHMATOV ³，Farkhod ESHMATOV ⁴

1.School of Mathematics, Sichuan University, Chengdu 610064, China；
2.School of Science, Chongqing University of Technology, Chongqing 400054, China；
3.Department of Mathematics and Statistics, University of Toledo, Toledo OH 43606, USA； 4.Beijing Advanced Innovation Center for Imaging Theory and Technology, Capital Normal University, Beijing 100048, China

Received:2020-03-04 Online:2020-09-25 Published:2020-09-25

Abstract

Abstract: Derived noncommutative algebraic geometry is one of the most active research fields in mathematics. Several important results that mathematicians have obtained in this field are reviewed, with an emphasis on the derived noncommutative symplectic structure, noncommutative Poisson structure, and their relationships with Calabi-Yau algebras and Calabi-Yau categories.

Key words: derived noncommutative geometry, noncommutative Poisson structure, noncommutative symplectic structure, Calabi-Yau category

CLC Number:

O186

CHEN Xiaojun, CHEN Youming, Alimjon ESHMATOV, Farkhod ESHMATOV. The shifted Poisson structure on derived representation schemes of Koszul Calabi-Yau algebras[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2020, 59(5): 1-18.

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The shifted Poisson structure on derived representation schemes of Koszul Calabi-Yau algebras

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