Representation theory of algebraic groups

Observable subgroup

In mathematics, in the representation theory of algebraic groups, an observable subgroup is an algebraic subgroup of a linear algebraic group whose every finite-dimensional rational representation arises as the restriction to the subgroup of a finite-dimensional rational representation of the whole group. An equivalent formulation, in case the base field is closed, is that K is an observable subgroup of G if and only if the quotient variety G/K is a quasi-affine variety. Some basic facts about observable subgroups: * Every normal algebraic subgroup of an algebraic group is observable. * Every observable subgroup of an observable subgroup is observable. (Wikipedia).

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Normal subgroups

Before we carry on with our coset journey, we need to discover when the left- and right cosets are equal to each other. The obvious situation is when our group is Abelian. The other situation is when the subgroup is a normal subgroup. In this video I show you what a normal subgroup is a

From playlist Abstract algebra

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Definition of a Subgroup in Abstract Algebra with Examples of Subgroups

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Subgroup in Abstract Algebra with Examples of Subgroups

From playlist Abstract Algebra

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Abstract Algebra | Normal Subgroups

We give the definition of a normal subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Quotient groups

The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under

From playlist Abstract algebra

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GT2. Definition of Subgroup

Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-

From playlist Abstract Algebra

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Subgroups abstract algebra

In this tutorial we define a subgroup and prove two theorem that help us identify a subgroup. These proofs are simple to understand. There are also two examples of subgroups.

From playlist Abstract algebra

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Group Theory: The Simple Group of Order 168 - Part 2

We show that there are no nontrivial normal subgroups in SL(3,Z/2). Techniques include Jordan canonical forms and companion matrices.

From playlist *** The Good Stuff ***

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Abstract Algebra | Cyclic Subgroups

We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Abstract Algebra | The notion of a subgroup.

We present the definition of a subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Commensurators of thin Subgroups by Mahan M. J.

PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.

From playlist Smooth And Homogeneous Dynamics

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Statistics: Collecting Data Exercises

This video covers sample, population, qualitative data, quantitative data, sampling methods, sampling bias, experimental and observational studies, and the types of experiments. http://mathispower4u.com

From playlist Introduction to Statistics

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Visual Group Theory, Lecture 3.6: Normalizers

Visual Group Theory, Lecture 3.6: Normalizers A subgroup H of G is normal if xH=Hx for all x in G. If H is not normal, then the normalizer is the set of elements for which xH=Hx. Obviously, the normalizer has to be at least H and at most G, and so in some sense, this is measuring "how clo

From playlist Visual Group Theory

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Pierre Emmanuel Caprace - Groups with irreducibly unfaithful subsets for unitary representations

A subset F of a group G is called irreducibly faithful if G has an irreducible unitary representation whose kernel does not contain any non-trivial element of F. We say that G has property P(n) if every subset of size at most n is irreducibly faithful. By a classical result o

From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette

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Visual Group Theory, Lecture 3.3: Normal subgroups

Visual Group Theory, Lecture 3.3: Normal subgroups A subgroup H of G is normal if every left coset gH equals the right coset Hg. In this lecture, we see several different ways of visualizing this concept as well as several equivalent definitions. We conclude with three useful but differen

From playlist Visual Group Theory

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Charles Rezk: Elliptic cohomology and elliptic curves (Part 3)

The lecture was held within the framework of the Felix Klein Lectures at Hausdorff Center for Mathematics on the 8. June 2015

From playlist HIM Lectures 2015

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Statistics Lecture 1.5: Sampling Techniques. How to Develop a Random Sample

https://www.patreon.com/ProfessorLeonard Statistics Lecture 1.5: Sampling Techniques. How to Develop a Random Sample

From playlist Statistics (Full Length Videos)

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Hyperbolic geometry, the modular group and Diophantine (Lecture - 01) by Shrikrishna G Dani

Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b

From playlist Geometry, Groups and Dynamics (GGD) - 2017

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Noa Dagan - Can we improve fairness for subpopulations by utilizing medical data? Pt. 2/2

Recorded 14 July 2022. Noa Dagan of Harvard Medical School presents "Can we improve fairness for subpopulations by utilizing medical data?" at IPAM's Graduate Summer School on Algorithmic Fairness. Abstract: Medical data can be utilized to promote proactive, predictive, and personalized ca

From playlist 2022 Graduate Summer School on Algorithmic Fairness

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Abstract Algebra | Quotient Groups

We introduce the notion of a quotient group and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Random groups I - Goulnara Arzhantseva

Women and Mathematics Title: Random groups Speaker: Goulnara Arzhantseva Affiliation: University of Vienna Date: May 16, 2017 For more videos, please visit http://video.ias.edu

From playlist Women and Mathematics 2017

Related pages

Subgroup | Algebraic group | Mathematics | Linear algebraic group | Normal subgroup | Rational representation | Representation theory