Lie groups | Finite reflection groups | Lie algebras
In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these. The Weyl group of a semisimple Lie group, a semisimple Lie algebra, a semisimple linear algebraic group, etc. is the Weyl group of the root system of that group or algebra. (Wikipedia).
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
A quick definition of groups on the periodic table. Chem Fairy: Louise McCartney Director: Michael Harrison Written and Produced by Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation
From playlist Chemistry glossary
Group theory 20: Frobenius groups
This lecture is part of an online mathematics course on group theory. It gives several examples of Frobenius groups (permutation groups where any element fixing two points is the identity).
From playlist Group theory
Chapter 5: Quotient groups | Essence of Group Theory
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory! In fac
From playlist Essence of Group Theory
Visual Group Theory, Lecture 1.6: The formal definition of a group
Visual Group Theory, Lecture 1.6: The formal definition of a group At last, after five lectures of building up our intuition of groups and numerous examples, we are ready to present the formal definition of a group. We conclude by proving several basic properties that are not built into t
From playlist Visual Group Theory
I've seen it a thousand times. You wanna do some transformation on a molecule, and it would work so wonderfully if this other functional group wasn't on the molecule to screw it up! You don't even want that other group to do any chemistry at all, isn't there some way to make it sit this ro
From playlist Organic Chemistry
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Weyl groups, and their generalizations in, enumerative geometry II - Okounkov
Hermann Weyl Lectures Topic: Weyl groups, and their generalizations in, enumerative geometry II Speaker: Andrei Okounkov Date: Wednesday, March 16 These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the firs
From playlist Hermann Weyl Lectures
Weyl groups, and their generalizations, in enumerative geometry I - Andrei Okounkov
Hermann Weyl Lectures Topic: Weyl groups, and their generalizations, in enumerative geometry I Speaker: Andrei Okounkov Date: Tuesday, March 15 These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lec
From playlist Hermann Weyl Lectures
David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Transport in topological junctions by Krishnendu Sengupta
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
Weyl Anomalies and Cosmology by Atish Dabholkar
11 January 2017 to 13 January 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru String theory has come a long way, from its origin in 1970's as a possible model of strong interactions, to the present day where it sheds light not only on the original problem of strong interactions, but
From playlist String Theory: Past and Present
What are Functional Groups? | Biology | Biochemistry
In biological molecules, the carbon skeleton determines their general 3D shape. But what’s on the surface of the molecules determines their chemical behavior. Small chemical species, hanging off the exterior of these molecules, bump into each other and react. These are known as FUNCTIONAL
From playlist Biology
Geometric graph theory: Weyl Groups, Root Systems and Quadratic Forms
In this video we explore the geometry of a graph coming from a combinatorial game. By playing the Mutation Game on populations on a graph, i.e. integer valued functions on the vertices, we can generate special populations which form a root system. In the ADE cases these are well-studied, f
From playlist MathSeminars
Yang Shi: Normalizer theory of Coxeter groups and discrete integrable systems
Abstract: Formulation of the Painleve equations and their generalisations as birational representations of affine Weyl groups provides us with an elegant and efficient way to study these highly transcendental, nonlinear equations. In particular, it is well-known that discrete evolutions of
From playlist Integrable Systems 9th Workshop
Euclid's elements: definitions, postulates, and axioms
This is a beginners introduction to Euclid's elements. Support my channel with this special custom merch! https://www.etsy.com/listing/1037552189/wooden-large-platonic-solids-geometry Learn step-by-step here: http://pythagoreanmath.com/euclids-elements/ visit my site: http://www.pythago
From playlist Euclid's Elements Book 1
Peter Jung: Some Aspects of Weyl Heisenberg Signal Design in Wireless Communication
Peter Jung: Some Aspects of Weyl Heisenberg Signal Design in Wireless Communication Abstract: Signal design using the structure of the Weyl-Heisenberg group is an important topic in several engineering disciplines. This includes, for example, pulse shaping for robust multicarrier transmis
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
Recent developments in Quantum Magnetism by Gang Chen
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)