報告題目：Killing metrized exact commutative algebras
報 告 人：Daniel Fox, Universidad Politécnica de Madrid
所在單位：Universidad Politécnica de Madrid
報告時間：2024年9月5日 20:00-22:00
Zoom Id: 904 645 6677，Password: 2024
會議鍊接：
https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
報告摘要: A commutative algebra is exact if the traces of its multiplication endormophisms vanish and it is Killing metrized if its Killing-type trace-form is invariant. Such an algebra is neither unital nor associative. Depending on one's background the class of Killing metrized exact commutative algebras may appear either absurdly special or so overbroad as to be hopeless to study. The extensive list of examples includes deunitalizations of étale associative algebras, deunitalizations of semisimple Jordan algebras, tensor products of semisimple Lie algebras, Griess algebras of certain vertex operator algebras, and certain algebras associated with combinatorial structures such as Steiner triple systems. I will motivate studying Killing metrized exact commutative algebras and explain some constructions based on an analogy between curvature of a connection and the associator of an algebra that can be used to organize their study. These will be used to classify algebras over general fields in dimensions at most four and to identify classes of Killing metrized exact commutative algebras susceptible to further study.
報告人簡介：Daniel Fox is a professor of mathematics at the Universidad Politécnica de Madrid in Spain.
