Журнал обобщенной теории лжи и ее приложений

Lie Theory: Historical review

Abstract

Charolette Smith

The hypothesis of Lie gatherings and their portrayals is a huge subject (Bourbaki [Bou] has so far composed 9 sections and 1,200 pages) with an unprecedented scope of utilizations. Probably the best mathematicians and physicists of our occasions have made the devices of the subject that we as a whole use. In this audit, I will talk about momentarily the advanced improvement of the subject from its verifiable beginnings during the nineteenth century. The causes of the Lie hypothesis are mathematical and come from the perspective of Felix Klein (1849–1925) that the calculation of room is dictated by the gathering of its balances. As the thought of room and its calculation advanced from Euclid, Riemann, and Grothendieck to the supersymmetric universe of the physicists, the ideas of Lie gatherings and their portrayals additionally extended correspondingly.