報告題目：Derivations on Operator Algebras and Quantum Dynamics
報 告 人：Shavkat Ayupov
所在單位：V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
報告時間：2024年9月21日 8:30-9:30
報告地點：吉林大學正新樓209
報告摘要: 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.
報告人簡介：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.
