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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 22 April 2026 - 13:30 to 14:30 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
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Speaker: Pierre Bieliavsky, UCLouvain<br />
Title: Kinematical Lie algebras and symplectic symmetric spaces
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Abstract <br />
<p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">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).</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">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 (</span><span style="background-color: rgb(255, 255, 255); color: rgb(68, 68, 68);">Bieliavsky, P., Boulanger, N.; Kinematical Lie algebras and symplectic symmetric spaces I. Lie algebraic aspects. Letters in Mathematical Physics, 116"(1), 2026). </span><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">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. </span></p><p class="ql-align-justify">-----------------------------------------------------------------------------------------------------------------------------------</p><p class="ql-align-justify"><span style="color: rgb(34, 34, 34); background-color: rgb(255, 255, 255);">We shall open ZOOM meeting at 13.15 for virtual coffee and close ZOOM at 15.30</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="color: rgb(34, 34, 34); background-color: rgb(255, 255, 255);">Join Zoom Meeting</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(17, 85, 204);">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="color: rgb(34, 34, 34); background-color: rgb(255, 255, 255);">Meeting ID:99598413922</span></p><p class="ql-align-justify"><span style="color: rgb(34, 34, 34); background-color: rgb(255, 255, 255);">Passcode:Galois</span></p><p>--------------------------------------------------------------------------------</p><p>On Wednesday April 29, Roee Leder shall give a talk on <a href="https://www.math.cas.cz/index.php/events/event/4193" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);"><strong>Cohomology for linearized Ricci curvature</strong></a></p><p><br></p><p><br></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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