生云鹤

姓名：

生云鹤

性别：

男

职称：

教授

所在系别：

基础数学系

是否博导：

是

最高学历：

研究生

最高学位：

博士

Email：

所在学科专业：

基础数学

所研究方向：

数学物理、Poisson几何、高阶李理论

讲授课程：

2009.09-2010.01, 空间解析几何, 2009基地班
2010.03-2010.07, 微分几何初步, 2007基础数学专业
2010.09-2011.01, 空间解析几何, 2010基地班+2010唐敖庆班
2011.03-2011.06, 黎曼几何,     2010级研究生
2011.08-2011.12, 李群在微分方程中的应用 2010级研究生
2011.09-2012.01, 空间解析几何, 2011基地班+2011唐敖庆班
2012.03-2012.06, 微分几何初步, 2009基础数学专业+基地班+唐班
2012.09-2013.01, 空间解析几何, 2012基地班+2011唐敖庆班
2013.03-2013.07, 微分几何初步, 2010基础数学专业+基地班+唐班
2013.09-2014.01, 空间解析几何, 2013基地班+2013唐敖庆班
2014.03-2014.07, 微分几何初步, 2011基础数学专业+基地班
2014.09-2015.01, 空间解析几何, 2014基地班+2014唐敖庆班
2014.09-2015.01, 黎曼几何,     2013级研究生
2015.09-2016.01, 空间解析几何, 2015级本科生
2016.09-2017.01, 空间解析几何, 2016级本科生
2016.08-2017.01, 微分几何几何, 2013级本科生数学与应用数学专业

教育经历：

2000.09-2004.07, js6668金沙登录入口
2004.09-2008.12, 北京大学数学学院       博士
2007.12-2008.11, Math. Dep. Utrecht Uni. Netherlands, joint Ph.D

工作经历：

2008.12-2009.07, CRC, Goettingen Uni. Post doctor
2009.01-2011.01, 大连理工大学数学学院 博士后
2009.06-2011.08     js6668金沙登录入口     副教授
2008.07.01-2008.07.12, Conference Poisson 2008, Bernnoulli Center, EPFL, Lausanne, Switzerland.
2010.07.02-2010.08.19, ANU, visiting scholar, Austrilia
2010.09.12-2010.09.19, Geometry and Physics VIII, Scalea, Italy
2012.06.27-2012.08.07, Goettingen Uni. visiting scholar, Germany
2012.07.22-2012.08.03, Conference Poisson 2012, Utrecht Uni., Holland
2013.06.21-2013.07.31, Goettingen Uni. visiting scholar, Germany
2013.06.25-2013.06.28, Conference Higher algebras and Lie-infinity homotopy theory, Luxembourg Uni., Luxembourg
2013.07.22-2013.07.26, Conference in honor of Alan Weinstein, Bernnoulli Center, EPFL, Lausanne, Switzerland.
2014.07.05-2014.07.24, Goettingen Uni. visiting scholar, Germany
2014.11.26-2014.12.10, Goettingen Uni. visiting scholar, Germany
2014.11.30-2014.12.06, Conference ;Algebra, deformation and quantum groups;, CIRM, France
2015.04.30-2015.05.16, Goettingen Uni. visiting scholar, Germany
2015.05.10-2015.05.15, Conference ;Geometry of Jets and Fields;, Bedlewo, Banach Center, Poland
2015.07.12-2015.08.07, Penn State University,  visiting scholar, US
2016.06.21-2016.07.23, University of Haute Alsace, visiting scholar, Mulhouse, France
2016.07.03-2016.07.09, Poisson 2016, Zurich,Switzerland.
2016.07.09-2016.07.17，Goettingen Uni. visiting scholar, Germany
2016.07.17-2016.07.21，Geneva Uni., visiting scholar,Switzerland.
2016.12.13-2017.12.12，Penn State University,  visiting scholar, US
2011.09-至今       js6668金沙登录入口     教授

科研项目：

博士后基金(20090451267，Courant代数胚的可积性) 2009.09-2011.01         负责人

数学天元基金（11026046，高阶李理论）2011.01-2011.12        负责人

博士点新教师基金（20100061120096，高阶李理论）2011.01-2013.12   负责人

国家自然科学基金青年基金（11101179，Poisson几何与高阶李理论 ）2012.01-2014.12    负责人

吉林省青年基金(20140520054JH，Courant代数胚与高阶结构)  2014.01-2016.12  负责人

国家自然科学基金面上项目(11471139，Poisson几何、高阶结构及其在数学物理中的应用)  2015.01-2018.12  负责人

吉林省自然科学基金（20170101050JC，Courant代数胚及其在数学物理中的应用） 2017.01-2019.12 负责人

国家自然科学基金优秀青年基金（11922110，数学物理） 2020.01-2022.12 负责人

国家自然科学基金面上项目（12471060，泊松几何与Rota-Baxter代数），2025.01-2028.12 负责人

学术论文：

[1] Y. Sheng, Linear Poisson structures on $\mathbb{R}^4$, J. Geom. Phys. 5 (2007), 2398-2410.

[2] Q. Lin, Z. Liu and Y. Sheng, Quadratic deformations of Lie-Poisson structures on $\mathbb{R}^3$, Lett. Math. Phys. 83 (2008), 217-229.

[3] Z. Chen, Z. Liu and Y. Sheng, E-Courant algebroids, Int. Math. Res. Not. (2010) No. 22, 4334-4376.

[4] Y. Sheng, Z. Liu and C. Zhu, Omni-Lie 2-algebras and their Dirac structures, J. Geom. Phys. 61(2011), 560-575.

[5] Y. Bi and Y. Sheng, On higher analogues of Courant algebroids, Sci. China Math. 54 (2011), No. 3, 437-447.

[6] S. Chen, Y. Sheng and Z. Zheng, Non-abelian Extensions of Lie 2-algebras, Sci. China Math. 55(2012), No. 8, 1655-1668.

[7] Y. Sheng and C. Zhu, Integration of Lie 2-algebras and their morphisms, Lett. Math. Phys. 102(2012), No. 2, 223-244.

[8] Y. Sheng, Representations of hom-Lie algebras, Algebr. Represent. Theory 15 (2012), No. 6, 1081-1098.

[9] Y. Sheng and D. Chen, Hom-Lie 2-algebras, J. Algebra 376 (2013), 174-195.

[10] C. Bai, Y. Sheng and C. Zhu, Lie 2-bialgebras, Comm. Math. Phys. 320 (2013), 149-172.

[11] Y. Sheng and C. Bai, A new approach to hom-Lie bialgebras, J. Algebra 399 (2014), 232-250.

[12] Z. Liu, Y. Sheng and T. Zhang, Deformations of Lie 2-algebras, J. Geom. Phys. 86 (2014), 66-80.

[13] Zhangju Liu, Yunhe Sheng, Xiaomeng Xu, The first Pontryagin class for Pre-Courant Algebroids, J. Geom. Phys. 104 (2016), 148-162.

[14] H. Lang, Y. Sheng and X. Xu, Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids, Lett. Math. Phys. 107 (2017), No. 5, 861-885.

[15] L. Cai, J. Liu and Y. Sheng, Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids, J. Geom. Phys. 121 (2017), 15-32.

[16] J. Liu, Y. Sheng and C. Bai, Pre-symplectic algebroids and their applications, Lett. Math. Phys. 108(2018), No. 3, 779-804.

[17] Y. Sheng and R. Tang, Symplectic, product and complex structures on 3-Lie algebras, J. Algebra508 (2018), 256-300.

[18] Y. Sheng, The first Pontryagin class of a quadratic Lie 2-algebroid, Comm. Math. Phys. 362 (2018), No. 2, 689-716.

[19] L. Cai and Y. Sheng, Purely Hom-Lie bialgebras, Sci. China Math. 61 (2018), No. 9, 1553-1566.

[20] C. Bai, L. Guo and Y. Sheng, Bialgebras, the classical Yang-Baxter equation and Manin triples for 3-Lie algebras, Adv. Theor. Math. Phys. 23 (2019), No. 1, 27-74.

[21] R. Tang, C. Bai, L. Guo and Y. Sheng, Deformations and their controlling cohomologies of $\mathcal{O}$-operators, Comm. Math. Phys. 368 (2019), 665-700.

[22] J. Liu, C. Bai and Y. Sheng, Compatible O-operators on bimodules over associative algebras, J. Algebra 532 (2019), 80-118.

[23] R. Tang, Y. Frégier and Y. Sheng, Cohomologies of a Lie algebra with a derivation and applications, J. Algebra 534 (2019), 65-99.

[24] R. Tang and Y. Sheng, Cohomological characterizations of non-abelian extensions of strict Lie 2-algebras, J. Geom. Phys. 144 (2019), 294-307.

[25] J. Liu and Y. Sheng, QP-structures of degree 3 and CLWX 2-algebroids, J. Symplectic Geom. 17(2019), No. 6, 1853-1891.

[26] J. Liu, C. Bai and Y. Sheng, Noncommutative Poisson bialgebras, J. Algebra 556 (2020), 35-66.

[27] J. Liu, Y. Sheng and C. Bai, $F$-manifold algebras and deformation quantization via pre-Lie algebras, J. Algebra 559 (2020), 467-495.

[28] R. Tang, S. Hou and Y. Sheng, Lie $3$-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras, J. Algebra 567 (2021), 37-62.

[29] J. Liu and Y. Sheng, Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids, J. Noncommutative Geom. 15 (2021), No. 1, 147-193.

[30] A. Lazarev, Y. Sheng and R. Tang, Deformations and homotopy theory of relative Rota-Baxter Lie algebras, Comm. Math. Phys. 383 (2021), 595-631.

[31] Y. Sheng, X. Xu and C. Zhu, String principal bundles and Courant algebroids, Int. Math. Res. Not. IMRN 2021, No. 7, 5290-5348.

[32] S. Hou, Y. Sheng and R. Tang, Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and $\mathcal{O}$-operators, J. Geom. Phys. 163 (2021), 104148, 1-15.

[33] L. Guo, H. Lang and Y. Sheng, Integration and geometrization of Rota-Baxter Lie algebras, Adv. Math. 387 (2021), 107834.

[34] Y. Sheng, R. Tang and C. Zhu, The controlling $L_\infty$-algebras, cohomologies and homotopy of embedding tensors and Lie-Leibniz triples, Comm. Math. Phys. 386 (2021), 269-304.

[35] J. Liu and Y. Sheng, Cohomologies of PoiMod pairs and compatible structures on Poisson algebras, J. Geom. Phys. 173 (2022), 104449.

[36] J. Jiang and Y. Sheng, Representations and cohomologies of relative Rota-Baxter Lie algebras and applications, J. Algebra 602 (2022), 637-670.

[37] R. Tang and Y. Sheng, Leibniz bialgebras, relative Rota-Baxter operators and the classical Leibniz Yang-Baxter equation, J. Noncommut. Geom. 16 (2022), No. 4, 1179-1211.

[38] J. Jiang and Y. Sheng, Deformations, cohomologies and integrations of relative difference Lie algebras, J. Algebra 614 (2023), 535-563.

[39] H. Lang and Y. Sheng, Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras, Comm. Math. Phys. 397 (2023), 763-791.

[40] S. Hou, Y. Sheng and Y. Zhou, 3-post-Lie algebras and relative Rota-Baxter operators of nonzero weights on $3$-Lie algebras, J. Algebra 615 (2023), 103-129.

[41] R. Tang and Y. Sheng, Nonabelian embedding tensors, Lett. Math. Phys. 113 (2023), 14.

[42] R. Tang, C. Bai, L. Guo and Y. Sheng, Homotopy Rota-Baxter operators and post-Lie algebras, J. Noncommut. Geom. 17 (2023), No. 1, 1-35.

[43] A. Lazarev, Y. Sheng and R. Tang, Homotopy relative Rota-Baxter Lie algebras, triangular $L_\infty$-bialgebras and higher derived brackets, Trans. Amer. Math. Soc. 376 (2023), 2921-2945.

[44] J. Liu, Y. Sheng and C. Bai, Maurer-Cartan characterizations and cohomologies of compatible Lie algebras, Sci. China Math. 66 (2023), No. 6, 1177-1198.

[45] Y. Sheng and Y. Wang, Quasi-triangular and factorizable antisymmetric infinitesimal bialgebras, J. Algebra 628 (2023), 415-433.

[46] Y. Pei, Y. Sheng, R. Tang and K. Zhao, Actions of monoidal categories and representations of Cartan type Lie algebras, J. Inst. Math. Jussieu 22 (2023), No. 5, 2367-2402.

[47] C. Bai, L. Guo, Y. Sheng and R. Tang, Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation, Math. Ann. 388 (2024), No. 3, 3127-3167.

[48] J. Jiang, Y. Sheng and C. Zhu, Lie theory and cohomology of relative Rota-Baxter operators, J. London Math. Soc. 109 (2024), No. 2, e12863.

[49] J. Jiang, Y. Li and Y. Sheng, Cohomologies of difference Lie groups and Van Est Theorem, J. Algebra 645 (2024), 116-142.

[50] Y. Wang, C. Bai, J. Liu and Y. Sheng, Quasi-triangular, factorizable pre-Lie bialgebras and Rota-Baxter pre-Lie algebras, J. Geom. Phys. 199 (2024), 105146.

[51] Y. Li, Y. Sheng and R. Tang, Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation, J. Noncommut. Geom. 18 (2024), No. 2, 605-630.

[52] R. Tang, N. Xu and Y. Sheng, Symplectic structure, product structures and complex structures on Leibniz algebras, J. Algebra 647 (2024), 710-743.

[53] S. Hou, Y. Sheng and Y. Zhou, Deformations, cohomologies and abelian extensions of compatible $3$-Lie algebras, J. Geom. Phys. 202 (2024), 105218.