Determine if the Binary Operation Defined by the Table is Commutative and Associative
In this video we determine whether or not a binary operation is commutative and associative. The binary operation is actually defined by a table in this example. I hope this video helps someone.
From playlist Abstract Algebra
Commutative and Associative Properties
My two favorite properties: the commutative and associative properties of multiplication and addition
From playlist Arithmetic
Matrix Theory: Let A be an nxn matrix with complex entries. We show that the commutant of A has dimension greater than or equal to n. The key step is to show the result for the Jordan canonical form of A.
From playlist Matrix Theory
EDIT: At 11:50, r^2(l-k) should be r^2l. At 14:05, index for top one should be n-2, not 2n-2. Abstract Algebra: We define the commutator subgroup for a group G and the corresponding quotient group, the abelianization of G. The main example is the dihedral group, which splits into tw
From playlist Abstract Algebra
You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.
From playlist Abstract algebra
Commutative algebra 27 (Associated primes)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We show that every finitely generated module M over a Noetherian ring R can broken up into modules of the form R/p for p prime
From playlist Commutative algebra
Commutative algebra 28 Geometry of associated primes
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give a geometric interpretation of Ass(M), the set of associated primes of M, by showing that its closure is the support Su
From playlist Commutative algebra
Commutative algebra 21 Tensor products and exactness
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we study when taking tensor product preserves exactness. We also show that tensor products preserve direct lim
From playlist Commutative algebra
A gentle description of a vertex algebra.
Working from the notions of associative algebras, Lie algebras, and Poisson algebras we build the idea of a vertex algebra. We end with the proper definition as well as an "intuition" for how to think of the parts. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation
From playlist Vertex Operator Algebras
Pre-recorded lecture 9: Homogeneous linear Nijenhuis operators and left-symmetric algebras
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Frédéric Patras - Noncommutative Wick Polynomials
Wick polynomials are at the foundations of QFT (they encode normal orderings) and probability (they encode chaos decompositions). In this lecture, we survey the construction and properties of noncommutative (or free) analogs using shuffle Hopf algebra techniques. Based on joint works wit
From playlist Combinatorics and Arithmetic for Physics: special days
Permutation Orbifolds of Vertex Operator Algebras
This is a recording of a talk I gave at the Illinois State University Algebra Seminar. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Websi
From playlist Research Talks
What is a Tensor? Lesson 19: Algebraic Structures I
What is a Tensor? Lesson 19: Algebraic Structures Part One: Groupoids to Fields This is a redo or a recently posted lesson. Same content, a bit cleaner. Algebraic structures are frequently mentioned in the literature of general relativity, so it is good to understand the basic lexicon of
From playlist What is a Tensor?
Kevin Buzzard (lecture 18/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
Nijenhuis Geometry Chair's Talk 2 (Alexey Bolsinov)
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Chair's Talk 2 (Alexey Bolsinov) 8 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 February 2022 Week
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Shane Farnsworth: Rethinking Connes' Approach to the Standard Model of Particle Physics via NCG
The preceding talk described a reformulation of Connes' non-commutative geometry (NCG), and some of its consequences for the NCG construction of the standard model of particle physics. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Ap
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Sergey Shadrin: Arnold's trinity of algebraic 2d gravitation theories
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: “Arnold’s trinities” refers to a metamathematical observation of Vladimir Arnold that many interesting mathematical concepts and theories occur in triples, with some
From playlist Noncommutative geometry meets topological recursion 2021
Commutative algebra 16 Localization
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we construct the localization R[S^-1] of a ring with respect to a multiplicative subset S, and give some examp
From playlist Commutative algebra
Ben Webster - Representation theory of symplectic singularities
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series