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)
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
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
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
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
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)
From playlist Summer of Math Exposition Youtube Videos
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
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
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
This lecture is part of an online course on category theory. We define functors and give some examples of them. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj51F9XZ_Ka4bLnQoxTdMx0AL
From playlist Categories for the idle mathematician
Kevin Coulembier: Frobenius exact tensor categories
Abstract: Partly motivated by Grothendieck’s original vision for motives, the question arises of when a tensor category (k-linear symmetric monoidal rigid abelian category) is tannakian, i.e. is the representation category of an affine group scheme, or more generally of a groupoid in schem
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
AMMI 2022 Course "Geometric Deep Learning" - Lecture 11 (Beyond Groups) - Petar Veličković
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 11: Category Theory • Set category • Functors • Natural
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the c
From playlist The New CHALKboard
A Hecke action on the principal block of a semisimple algebraic group - Simon Riche
Workshop on Representation Theory and Geometry Topic: A Hecke action on the principal block of a semisimple algebraic group Speaker: Simon Riche Affiliation: Université Paris 6; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Towards a modular "2 realizations" equivalence - Simon Riche
Geometric and Modular Representation Theory Seminar Topic: Towards a modular "2 realizations" equivalence Speaker: Simon Riche Affiliation: Université Clermont Auvergne; Member, School of Mathematics Date: May 05, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Frobenius exact symmetric tensor categories - Pavel Etingof
Geometric and Modular Representation Theory Seminar Topic: Frobenius exact symmetric tensor categories Speaker: Pavel Etingof Affiliation: Massachusetts Institute of Technology Date: May 12, 2021 For more video please visit https://www.ias.edu/video
From playlist Seminar on Geometric and Modular Representation Theory
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Yonatan Harpaz - New perspectives in hermitian K-theory II
Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an
From playlist New perspectives on K- and L-theory