Representation theory of algebraic groups
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).
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
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
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
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
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
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
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 ***
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
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
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
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
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
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
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
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
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)
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
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
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
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