BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pierre Bieliavsky (UCLouvain) DTSTART:20260422T113000Z DTEND:20260422T123000Z DTSTAMP:20260430T190654Z UID:PHK-cohomology-seminar/154 DESCRIPTION:Title: Kinematical Lie algebras and symplectic symmetric spaces< /a>\nby Pierre Bieliavsky (UCLouvain) as part of Prague-Hradec Kralove sem inar Cohomology in algebra\, geometry\, physics and statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\nThe notion of kinematical Lie algebra w as introduced in physics for the classification of the various possible re lativity algebras an isotropic spacetime can accommodate (H. Bacry and J. Levy-Leblond. Possible kinematics. J. Math. Phys.\, 9\; 1968). Kinematical Lie algebras were classified in spacetime dimension four by brute force i n the middle of the eighties. (H. Bacry and J. Nuyts. Classification of Te n-dimensional Kinematical Groups With Space Isotropy. J. Math. Phys.\, 27\ ; 1986). More recently\, those were reconsidered in a much wider context w ithin the mathematical framework of Cartan geometry (José Figueroa-O'Farr ill. Non-lorentzian spacetimes. Differ. Geom. Appl.\, 82\; 2022).\n\nIn a joint work with N. Boulanger (UMons)\, we recently gave an elementary proo f of the fact that such a kinematical Lie algebra (and natural generalizat ions) always carries a canonical structure of symplectic involutive Lie al gebra i.e. consists in the tangent version of a very specific class of sym plectic symmetric spaces i.e. affine symmetric spaces equipped with parall el symplectic structures (Bieliavsky\, P.\, Boulanger\, N.\; Kinematical L ie algebras and symplectic symmetric spaces I. Lie algebraic aspects. Lett ers in Mathematical Physics\, 116"(1)\, 2026). This geometrical result yie lds in particular an alternative classification of (generalized) kinematic al Lie algebras of arbitrary dimension in purely symplectic geometric term s. It also establishes an unexpected strong relation between these spaceti mes and contact sub-Riemannian symmetric spaces. In the talk\, after havin g introduced the basic notions\, I will explain these results. If time per mits\, I will show the implications within the currently fastly developing field of geometric actions.\n LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/154/ END:VEVENT END:VCALENDAR