刘玉明 - 北京师范大学 - 数学科学学院

个人简介

09.2020 - 01.2021 One semester teaching on Algebra, Beijing Normal University at Zhuhai. 02.2018 - 08.2018 Renewed Humboldt Research, Institute of Algebra and Number Theory, University of Stuttgart. (host: Prof. Steffen Koenig) 02.2014 ESCAP Project, LAMFA, Université de Picardie. (host: Prof. Alexander Zimmermann) 07.2012 - 10.2012 Renewed Humboldt Research, Institute of Algebra and Number Theory, University of Stuttgart. (host: Prof. Steffen Koenig) 07.2009 - Associate Professor, School of Mathematical Sciences, Beijing Normal University. 10.2007 - 08.2009 Marie Curie Fellowship, Mathematisches Institut, Universitaet zu Koeln. (host: Prof. Steffen Koenig) 08.2006 - 09.2007 Alexander von Humboldt Fellow, Mathematisches Institut, Universitaet zu Koeln. (host: Prof. Steffen Koenig) 10.2005 - 02.2006 Leverhulme Fellowship, Mathematisches Institut, Universitaet zu Koeln. (host: Prof. Steffen Koenig) 08.2004 - 06.2009 Lecturer, School of Mathematical Sciences, Beijing Normal University. 09.2001 - 06.2004 PhD Student, School of Mathematical Sciences, Beijing Normal University. 09.1998 - 06.2001 Master Student, Department of Mathematics, Beijing Normal University. 07.1993 - 08.1998 Teaching Assistant, Department of Mathematics, Qinghai Normal College. 09.1989 - 06.1993 Undergraduate Student, Department of Mathematics, Shaanxi Normal University.

研究领域

表示论是抽象代数中的一个分支。它的方法是把抽象的代数对象（比如群、环、代数等）用某种具体的研究对象（比如矩阵、多项式等）表示出来，并由此揭示原来对象的结构和性质。例如，通过一个同态映射，我们可以把一个环与一个具体的矩阵环联系起来，这就给出了这个环的一个“表示”（或者说是给出了这个环上的一个模）。一个环有许许多多不同的表示，其中有些是基本的表示，它们包含着原来代数的重要信息。如果我们把这个环的所有表示拿来放在一起，就构成了这个环的“表示的范畴”。表示的范畴一般具有十分丰富的（代数的、几何的或分析的）结构，它们不但能反映环的各种（代数的、同调的、组合的或几何的）特性，还常常能建立与其它数学领域意想不到的联系。比如，代数表示论中著名的Gabriel定理建立了表示有限型遗传环的表示范畴与复半单李代数的深刻联系。我的研究方向是有限维代数的表示理论，关心的课题有：稳定范畴和稳定等价，导出等价，Tate-Hochschild上同调等。这方面目前有许多基本的理论问题尚未解决（例如关于稳定等价的Auslander-Reiten猜想、单纯系统的构造等）。

近期论文

查看导师新发文章（温馨提示：请注意重名现象，建议点开原文通过作者单位确认）

The Hochschild cohomology groups under gluing idempotents (with L. Rubio y Degrassi and C. Wen) Revised (2023), 1-33. Algebraic Morse theory via homological perturbation lemma with applications to Chinese algebras (with J. Chen and G. D. Zhou) Revised (2023), 1-28. The liftability question for stable equivalences between representation-finite self-injective algebras (with N. Q. Li) Algebr. Represent. Theor. (2022), https://doi.org/10.1007/s10468-022-10141-6. On simple-minded systems over representation-finite self-injective algebras (with J. Guo, Y. Ye and Z. Zhang) Algebr. Represent. Theor. 25 (2022), 983-1002. An explicit construction of simple-minded systems over self-injective Nakayama algebras (with J. Guo, Y. Ye and Z. Zhang) Colloq. Math. 164 (2021), 185-210. A computer program by Wenting Huang On simple-minded systems and $\tau$-periodic modules of self-injective algebras (with A. Chan and Z. Zhang) J. Algebra 560 (2020), 416-441. The Batalin-Vilkovisky structure on the Tate-Hochschild cohomology ring of a group algebra (with Z. F. Wang and G. D. Zhou) IMRN, 2021(6) (2021), 4079-4139. The associated graded algebras of Brauer graph algebras I: finite representation type (with J. Guo) Comm. in Algebra 49(3) (2021), 1071-1103. Two questions on stable equivalences of Morita type (with G. D. Zhou and A. Zimmermann) Proc. Amer. Math. Soc. 145(5) (2017), 1881-1890. The Batalin-Vilkovisky structure over the Hochschild cohomology ring of a group algebra A MAPLE program (with G. D. Zhou) J. Noncommut. Geom. 10 (2016), 811-858. Simple-minded systems, configurations and mutations for representation-finite self-injective algebras (with A. Chan and S. Koenig) J. Pure. Appl. Algebra 219 (2015), 1940-1961. On simple-minded system and \tau-invariant modules (with A. Chan) Preprint (2016), 1-9. Simple-minded systems in stable module categories corrections (with S. Koenig) Quarterly J. Math. 63 (3) (2012), 653-674. Transfer maps in Hochschild (co)homology and applications to stable and derived invariants and to the Auslander-Reiten conjecture (with S. Koenig and G. D. Zhou) Trans. Amer. Math. Soc. 364 (2012), 195-232. Higman-ideal, stable Hochschild homology and Auslander-Reiten conjecture (with G. D. Zhou and A. Zimmermann) Math. Zeit. 270 (2012), 759-781. Some new developments on stable equivalences of Morita type (with C. C. Xi) Advances in Mathematics (Chinese) 37(4) (2008), 385-391. Summands of stable equivalences of Morita type Comm. in Algebra 36(10) (2008), 3778-3782. Gluing of idempotents, radical embeddings and two classes of stable equivalences corrections (with S. Koenig) J. Algebra 319(12) (2008), 5144-5164. Constructions of stable equivalences of Morita type for finite dimensional algebras III (with C. C. Xi) Jour. Lon. Math. Soc. 76(3) (2007), 567-585. On stable equivalences induced by exact functors Proc. Amer. Math. Soc. 134 (2006), 1605-1613. Construction of stable equivalences of Morita type for finite dimensional algebras I (with C. C. Xi) Trans. Amer. Math. Soc. 358 (2006), 2537-2560. Constructions of stable equivalences of Morita type for finite dimensional algebras II (with C. C. Xi) Math. Zeit. 251 (2005), 21-39. On stable equivalences of Morita type for finite dimensional algebras Proc. Amer. Math. Soc. 131 (2003), 2657-2662.