Algebraic groups

Pseudo-reductive group

In mathematics, a pseudo-reductive group over a field k (sometimes called a k-reductive group) is a smooth connected affine algebraic group defined over k whose k-unipotent radical (i.e., largest smooth connected unipotent normal k-subgroup) is trivial. Over perfect fields these are the same as (connected) reductive groups, but over non-perfect fields Jacques Tits found some examples of pseudo-reductive groups that are not reductive. A pseudo-reductive k-group need not be reductive (since the formation of the k-unipotent radical does not generally commute with non-separablescalar extension on k, such as scalar extension to an algebraic closure of k). Pseudo-reductive groups arise naturally in the study of algebraic groups over function fields of positive-dimensional varieties in positive characteristic (even over a perfect field of constants). gives an exposition of Tits' results on pseudo-reductive groups, while builds on Tits' work to develop a general structure theory, including more advanced topics such as construction techniques, root systems and root groups and open cells, classification theorems, and applications to rational conjugacy theorems for smooth connected affine groups over arbitrary fields. The general theory (with applications) as of 2010 is summarized in , and later work in the second edition and in provides further refinements. (Wikipedia).

Video thumbnail

Redneck Machinists | Rocket City Rednecks

The redneck geniuses get to work building a hydro-powered boat. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photographers, journa

From playlist Rocket City Rednecks: Season 1

Video thumbnail

Redneck Code Red | Rocket City Rednecks

Travis and Michael get into some trouble after diving deep. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photographers, journalist

From playlist Rocket City Rednecks: Season 1

Video thumbnail

Watermelon Defense | Rocket City Rednecks

Travis creates a homemade robot wielding a shotgun to defend the world from an incoming watermelon — er, um, space rock. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Th

From playlist Rocket City Rednecks: Season 1

Video thumbnail

Super Cow Creators | | National Geographic

Extreme Genes: These gigantic cows resemble bovine body-builders. See how breeders have achieved such amazing results. ➡ Subscribe: http://bit.ly/NatGeoSubscribe ➡ Access our digital archive by becoming a member of National Geographic: https://on.natgeo.com/2ZJFecu #NationalGeographic #Co

From playlist Trending Videos | National Geographic

Video thumbnail

Backwoods Paintball | Rocket City Rednecks

Paintball is the perfect way to put the rednecks' spy balloon to the test. And the winner gets a cooler full of beer! ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Thro

From playlist Rocket City Rednecks: Season 1

Video thumbnail

The Evolution of the Vigilante | The March on Washington

After the emancipation of slaves in the united states there was an increase of vigilante groups across the country. These groups included organizations such as the Ku Klux Klan and the Knights of the White Camelia, and they behaved as if they were a reinforcement of the law. ➡ Subscribe: h

From playlist News | National Geographic

Video thumbnail

Pseudo-reductive groups by Brian Conrad

PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will

From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)

Video thumbnail

Tamagawa Numbers of Linear Algebraic Groups over (...) - Rosengarten - Workshop 2 - CEB T2 2019

Zev Rosengarten (Hebrew University of Jerusalem) / 26.06.2019 Tamagawa Numbers of Linear Algebraic Groups over Function Fields In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply con

From playlist 2019 - T2 - Reinventing rational points

Video thumbnail

Hydroxyl-directed 1,3 Reductions of Ketones - Organic Chemistry, Reaction Mechanism

Three named reactions in organic chemistry that are highly diastereoselective reductions of beta-hydroxyketones. This video discussed the synthetic chemistry aspects and the appropriate transition states for these kinetically controlled reactions. #chemistry #organicchemistry #orgo #ochem

From playlist Organic Chemistry Mechanisms

Video thumbnail

Solar-Powered Redneck Engine | Rocket City Rednecks

The rednecks have a new plan to power Daddy's bass boat with a homemade solar-powered engine. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class sci

From playlist Rocket City Rednecks: Season 1

Video thumbnail

Moduli of Representations and Pseudorepresentations - Carl Wang Erickson

Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli

From playlist Mathematics

Video thumbnail

CBS Reduction, Enantioselective Catalysis - Organic Chemistry, Reaction Mechanism

Another introductory video on enantioselective catalysis in Organic Chemistry. Here secondary ketones can be synthesised in high enantiomeric excess from the parent ketone by a CBS reduction reaction. Essentially the CBS reduction is a chiral version of the more familiar reagent sodium bor

From playlist Organic Chemistry Mechanisms

Video thumbnail

Talk by Rahul Dalal (University of California, Berkeley, USA)

Statistics of Automorphic Representations Through the Stable Trace Formula

From playlist Seminars: Representation Theory and Number Theory

Video thumbnail

The surprising behaviour that stunned scientists - BBC REEL

Scientists have discovered a unique behaviour among the Indo-Pacific bottlenose dolphins in the Red Sea. The dolphins deliberately rub themselves through the fronds of a bush-like coral called a gorgonian. Researchers now believe this to be a form of self-medication that could unlock the s

From playlist Secret Worlds

Video thumbnail

Rod Gover - An introduction to conformal geometry and tractor calculus (Part 3)

After recalling some features (and the value of) the invariant « Ricci calculus » of pseudo­‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

Video thumbnail

Plenary lecture 1 by Martin Bridson - Part 2

Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma

From playlist Geometry Topology and Dynamics in Negative Curvature

Video thumbnail

João Lourenço: Twisted Kac-Moody groups over the integers

In geometric representation theory, one is interested in studying the geometry of affine Grassmannians of quasi-split simply-connected reductive groups. In this endeavor, one of the main techniques, introduced by Faltings in the split case, consists in constructing natural realisati

From playlist Algebraic and Complex Geometry

Video thumbnail

Redneck Satellite | Rocket City Rednecks

The rednecks find a satellite dish large enough to help them make a homemade interferometer. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scie

From playlist Rocket City Rednecks: Season 1

Video thumbnail

Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics

Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories « at infinity », to the asymptotic phenomena of an interior (pseudo‐)‐Riemannian geometry of one higher dimension. It provides an effective

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

Related pages

Reductive group | Perfect field | Ree group | Field (mathematics)