BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Heon Lee (Harbin Institute of Technology\, China) DTSTART:20250407T120000Z DTEND:20250407T130000Z DTSTAMP:20260422T182333Z UID:QGS/129 DESCRIPTION:Title: Fi rst-order differential calculi and Laplacians on $q$-deformations of compa ct semisimple Lie groups\nby Heon Lee (Harbin Institute of Technology\ , China) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn this ta lk\, we suggest a simple definition of Laplacian on a compact quantum grou p (CQG) associated with a first-order differential calculus (FODC) on it. Applied to the classical differential calculus on a compact Lie group\, th is definition yields classical Laplacians\, as it should. Moreover\, on th e CQG $ K_q $ arising from the $ q $-deformation of a compact semisimple L ie group $K$\, we can find many interesting linear operators that satisfy this definition\, which converge to a classical Laplacian on $ K $ as $ q $ tends to 1. In the light of this\, we call them $ q $-Laplacians on $ K_ q $ and investigate some of their operator theoretic properties. In partic lar\, we show that the heat semigroups generated by these are not complete ly positive\, suggesting that perhaps on the CQG $ K_q $\, stochastic proc esses that are most relevant to the geometry of it are not quantum Markov processes. This work is based on the preprint arXiv:2410.00720.\n LOCATION:https://researchseminars.org/talk/QGS/129/ END:VEVENT END:VCALENDAR