BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Stewart (University of Manchester\, UK) DTSTART:20250106T150000Z DTEND:20250106T160000Z DTSTAMP:20260423T021121Z UID:ENAAS/105 DESCRIPTION:Title: Geometric rigidity of modules for algebraic groups\nby David Stewart ( University of Manchester\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nLet k be a field\, let G be a smooth affine k-grou p of finite type\, and V a finite-dimensional G-module. We say V is rigid if the socle series and radical series coincide for the action of G on eac h indecomposable summand of V\; say V is geometrically rigid (resp. absolu tely rigid) if V is rigid after base change of G and V to an algebraic clo sure of k (resp. any field extension of k). We show that all simple G-modu les are geometrically rigid\, though they are not in general absolutely ri gid. More precisely\, we show that if V is a simple G-module\, then there is a finite purely inseparable extension k_V /k naturally attached to V su ch that V_{k_V} is absolutely rigid as a G_{k_V} -module. The proof for co nnected G turns on an investigation of algebras of the form K \\otimes_k E where K and E are field extensions of k\; we give an example of such an a lgebra which is not rigid as a module over itself. We establish the existe nce of the purely inseparable field extension k_V /k through an analogous version for Artinian algebras.\n LOCATION:https://researchseminars.org/talk/ENAAS/105/ END:VEVENT END:VCALENDAR