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湖州師范學院黨委宣傳部、新聞中心主辦

數學學科2020系列學術報告之七、八

來源:理學院 發布日期:2020-06-28

報告人:生云鶴,吉林大學,國家優秀青年基金獲得者。

Title: Deformations of O-operators on Leibniz algebras and Leibniz bialgebras

時間:2020/7/1 14:30-15:30   地點:騰訊會議:

https://meeting.tencent.com/s/8uX6TujWDPGu

會議 ID:689 492 999

摘要:In this talk, we study (proto-, quasi-)twilled Leibniz algebras and the associated L-infty-algebras and differential graded Lie algebras. As applications, first we study   the twilled Leibniz algebra corresponding to the semidirect product of a Leibniz algebra and its representation. We show that O-operators  on this Leibniz algebra can be characterized as Maurer-Cartan elements of the associated gLa. Furthermore, an O-operator will give rise to a dgLa that can control its deformations. Then we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, quadratic twilled Leibniz algebras and Leibniz bialgebras are equivalent. We further define classical Leibniz-Yang-Baxter equation, classical Leibniz r-matrix and  triangular Leibniz bialgebra using  the associated gLa and the twisting theory of twilled Leibniz algebras. We introduce the notion of a Leibniz-dendriform algebra as the algebraic structure underlying an O-operator, by which we can construct  solutions  of the classical Leibniz-Yang-Baxter equation.

報告人簡介:生云鶴,男,吉林大學數學學院教授、博士生導師、基礎數學系主任。2004年6月畢業于吉林大學,獲理學學士學位;2008年12月畢業于北京大學,獲理學博士學位,2007年12月至2008年11月荷蘭烏特列支大學數學系聯合培養;2008年12月至2009年8月德國哥廷根大學博士后。主要研究領域為Poisson幾何、非線性李理論、高階李理論。在Comm. Math. Phys.、Int. Math. Res. Not. IMRN、Transform. Groups、J. Algebra、Pacific J. Math.等著名期刊發表學術論文50余篇。主持國家自然科學基金委優秀青年基金、面上項目等多項國家級和省部級項目。




報告人:陳良云,東北師范大學

題目:Derivations, Biderivations,triple derivations and  triple homomorphisms on Jordan algebras

時間:2020/7/1 15:30-16:30, 地點:騰訊會議

摘要:In this talk, we mainly study derivations, biderivations and triple derivations on Jordan algebras. Firstly, the sufficient and necessary conditions for their derivation algebras being simple are given. As an application, triple derivations of derivation algebras of semi-simple Jordan algebras are studied. Then we give a theorem about the relationship between biderivations and centroid of Jordan algebras and show that triple derivations are all derivations on Jordan algebras under some assumptions. Moreover, we also give a theorem about triple homomorphisms on Jordan algebras. This talk is a report on joint work with Yao Ma and Chenrui Yao.

報告人簡介:  陳良云,東北師范大學數學與統計學院三級教授、博士生導師、博士后合作導師。南開大學理學博士、哈爾濱工業大學博士后、東京大學博士后。吉林省拔尖創新人才、吉林省教育廳新世紀優秀人才、長春市有突出貢獻專家,省級精品課負責人。主要研究方向是李超代數及其應用,發表90余篇SCI論文。曾主持4項國家自然科學基金、4項省部級項目。指導博士和博士后20余人、碩士60余人,其中2名博士和3名碩士獲吉林省優秀學位論文。擔任《山東大學學報》(理學版)、《海南熱帶海洋學院學報》及6個外國期刊編委,國家自然科學基金委員會、萬人計劃領軍人才、國家博士后基金同行評議專家,吉林省自然科學基金評審組專家。

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