报告题目：Derivations on Operator Algebras and Quantum Dynamics

报 告 人：Shavkat Ayupov

所在单位：V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences

报告时间：2024年9月21日 8:30-9:30

报告地点：吉林大学正新楼209

报告摘要: This talk presents a full resolution of the problem stated by Ayupov in 2000, and partly restated in 2014 by Kadison and Liu, concerning derivations on algebras of measurable operators aﬃliated with von Neumann algebras. First we give preliminaries from the theory of operator algebras, non-commutative integration theory and show the physical background of automorphisms and derivations on operator algebras. The second part of the talk explains a background of the Ayupov-Kadison-Liu Problem and its connection with general derivation theory in operator algebras starting with fundamental results due to Kaplanski, Kadison, Sakai and others. We shall cite and brieﬂy explain major results concerning derivations on algebras of unbounded operators and list results concerning some special cases of the problem. Finally, the main result yielding the full resolution will be stated.

报告人简介：Shavkat Ayupov is the Director of V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences. His field of scientific interest include Theory of Operator Algebras and Quantum Probability, Structure theory of Non-associative algebras (Jordan, Lie, Leibniz, etc.). He is the authors of several monograph devoted to Real and Jordan structures on Operator Algebras, also to the structure theory of Leibniz algebras. Sh. Ayupov is a Member of Uzbekistan Academy of Sciences (since 1995), Fellow of TWAS (The World Academy of Sciences) (since 2003), Senior Associate of ICTP (International Centre for Theoretical Physics) (2008 – 2013), Guest Professor of Sichuan University (Chengdu, China) (2015-2021). He is the Managing Editor of Uzbek Mathematical Journal and editor of “Advances in Operator Theory”. In 2017, he was awarded the State Prize of the first degree in the field of Science and Technology of the Republic of Uzbekistan.