[PHK_seminar] [Cohomology]Wednesday 22 Apr, Pierre Bieliavsky

[Igor Khavkine]

Dear All,

The video recording of the talk by Pierre Bieliavsky from last week is 
now available on YouTube at

   https://youtu.be/nVzWtSY5Yb8

The slides are available from

  
https://users.math.cas.cz/~hvle/PHK/BieliavskykinematicalLiealgebras2026.pdf

Both links have also been recorded at the ResearchSeminars announcement

   https://researchseminars.org/talk/PHK-cohomology-seminar/154/

Best,

Igor

On 4/20/26 1:00 PM, sender of seminar announcement via phk_seminar wrote:
> Wednesday, 22 April 2026 - 13:30 to 14:30
> Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
> 
> Speaker: Pierre Bieliavsky, UCLouvain
> Title: Kinematical Lie algebras and symplectic symmetric spaces
> 
> Abstract
> 
> The notion of kinematical Lie algebra was introduced in physics for the 
> classification of the various possible relativity 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 in the middle of 
> the eighties. (H. Bacry and J. Nuyts. Classification of Ten-dimensional 
> Kinematical Groups With Space Isotropy. J. Math. Phys., 27; 1986). More 
> recently, those were reconsidered in a much wider context within the 
> mathematical framework of Cartan geometry (José Figueroa-O'Farrill. Non- 
> lorentzian spacetimes. Differ. Geom. Appl., 82; 2022).
> 
> In a joint work with N. Boulanger (UMons), we recently gave an 
> elementary proof of the fact that such a kinematical Lie algebra (and 
> natural generalizations) always carries a canonical structure of 
> symplectic involutive Lie algebra i.e. consists in the tangent version 
> of a very specific class of symplectic symmetric spaces i.e. affine 
> symmetric spaces equipped with parallel symplectic structures 
> (Bieliavsky, P., Boulanger, N.; Kinematical Lie algebras and symplectic 
> symmetric spaces I. Lie algebraic aspects. Letters in Mathematical 
> Physics, 116"(1), 2026). This geometrical result yields in particular an 
> alternative classification of (generalized) kinematical Lie algebras of 
> arbitrary dimension in purely symplectic geometric terms. It also 
> establishes an unexpected strong relation between these spacetimes and 
> contact sub-Riemannian symmetric spaces. In the talk, after having 
> introduced the basic notions, I will explain these results. If time 
> permits, I will show the implications within the currently fastly 
> developing field of geometric actions.
> 
> -----------------------------------------------------------------------------------------------------------------------------------
> 
> We shall open ZOOM meeting at 13.15 for virtual coffee and close ZOOM at 
> 15.30
> 
> 
> Join Zoom Meeting
> 
> 
> https://cesnet.zoom.us/j/99598413922? 
> pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09 <https://cesnet.zoom.us/ 
> j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09>
> 
> 
> Meeting ID:99598413922
> 
> Passcode:Galois
> 
> --------------------------------------------------------------------------------
> 
> On Wednesday April 29, Roee Leder shall give a talk on *Cohomology for 
> linearized Ricci curvature* <https://www.math.cas.cz/index.php/events/ 
> event/4193>
> 
> 
> 
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
> 
> Cohomology in algebra, geometry, physics and statistics mailing list
> phk_seminar at math.cas.cz
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
> 
> 
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