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
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Group automorphisms in abstract algebra
Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem
From playlist Abstract algebra
Claudia Pinzari: "Weak quasi-Hopf algebras associated to Verlinde fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Weak quasi-Hopf algebras associated to Verlinde fusion categories" Claudia Pinzari - Sapienza Università di Roma Abstract: Unitary modular fusion categories arise in various frameworks. After a general overview on unitarity, we discuss th
From playlist Actions of Tensor Categories on C*-algebras 2021
Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties
The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra
Inna Entova-Aizenbud: Jacobson-Morozov Lemma for Lie superalgebras using semisimplification
I will present a generalization of the Jacobson-Morozov Lemma for quasi-reductive algebraic supergroups (respectively, Lie superalgebras), based on the idea of semisimplification of tensor categories, which will be explained during the talk. This is a joint project with V. Serganova.
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
All About Subgroups | Abstract Algebra
We introduce subgroups, the definition of subgroup, examples and non-examples of subgroups, and we prove that subgroups are groups. We also do an example proving a subset is a subgroup. If G is a group and H is a nonempty subset of G, we say H is a subgroup of G if H is closed with respect
From playlist Abstract Algebra
Moduli of p-divisible groups (Lecture 1) by Ehud De Shalit
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Group Isomorphisms in Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Isomorphisms in Abstract Algebra - Definition of a group isomorphism and isomorphic groups - Example of proving a function is an Isomorphism, showing the group of real numbers under addition is isomorphic to the group of posit
From playlist Abstract Algebra
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Cyclic groups are first and foremost, as the term implies, groups. What makes them cyclic is that at least on of the elements in the set that makes up the group under a specific binary operation can generate the group by performing the binary operation on itself. So, if a is an element o
From playlist Abstract algebra
Pablo Linares & Markus Tempelmayr - A tree-free construction of the structure group
We present a new approach to regularity structures, and in particular to the construction of the structure group, which replaces the tree-based framework of Hairer by a more Lie-geometric setting. We consider the space of pairs (a,p), where a is a placeholder for the nonlinearity and p is
From playlist Research Spotlight
Duality for polygons and the Fundamental theorem of Algebra | Algebraic Topology | NJ Wildberger
We define the dual of a polygon in the plane with respect to a fixed origin and unit circle. This duality is related to the notion of the dual of a cone. Then we give a purely rational formulation of the Fundamental Theorem of Algebra, and a proof which keeps track of the winding number of
From playlist Algebraic Topology
MAE5790-17 Chaos in the Lorenz equations
Global stability for the origin for r is less than 1. Liapunov function. Boundedness. Hopf bifurcations. No quasiperiodicity. Simulations of the Lorenz system. Stories of how Lorenz made his discovery. Strange attractor and butterfly effect. Exponential divergence of nearby trajectories. L
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
Symmetries of hamiltonian actions of reductive groups - David Ben-Zvi
Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II - Amnon Ta-Shma Computer Science/Discrete Mathematics Seminar II Topic: Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II Speaker: Amnon Ta-Shma Affiliation: Tel Aviv University Date: January 3
From playlist Mathematics
Every Cyclic Group is Abelian | Abstract Algebra
We prove every cyclic group is abelian by taking two arbitrary elements from an arbitrary cyclic group and showing they commute. Recall a cyclic group is entirely generated by all powers of a particular element. #abstractalgebra #grouptheory Cyclic Groups, Generators, and Cyclic Subgroup
From playlist Abstract Algebra
Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction - Mikhail Kapranov
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction Speaker: Mikhail Kapranov Affiliation: Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo Dat
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory