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
Shun-Jen Cheng: Representation theory of exceptional Lie superalgebras
SMRI Algebra and Geometry Online: Shun-Jen Cheng (Institute of Mathematics, Academia Sinica) Abstract: In the first half of the talk we shall introduce the notion of Lie superalgebras, and then give a quick outline of the classification of finite-dimensional complex simple Lie superalgebr
From playlist SMRI Algebra and Geometry Online
Serganova, Vera, Lecture V - 3 February 2015
Vera Serganova (University of California, Berkeley) - Lecture V http://www.crm.sns.it/course/4034/ The goal of this minicourse is to review recent results in representation theory of finite-dimensional Lie superalgebras. Lecture 1 Finite-dimensional Lie superalgebras: classification, exam
From playlist Lie Theory and Representation Theory - 2015
Serganova, Vera, Lecture IV - 28 January 2015
Vera Serganova (University of California, Berkeley) - Lecture IV http://www.crm.sns.it/course/4034/ The goal of this minicourse is to review recent results in representation theory of finite-dimensional Lie superalgebras. Lecture 1 Finite-dimensional Lie superalgebras: classification, exa
From playlist Lie Theory and Representation Theory - 2015
Serganova, Vera, Lecture III - 26 January 2015
Vera Serganova (University of California, Berkeley) - Lecture III http://www.crm.sns.it/course/4034/ The goal of this minicourse is to review recent results in representation theory of finite-dimensional Lie superalgebras. Lecture 1 Finite-dimensional Lie superalgebras: classification, ex
From playlist Lie Theory and Representation Theory - 2015
Vera Serganova, Lecture I - 20 January 2015
Vera Serganova (University of California, Berkeley) - Lecture I http://www.crm.sns.it/course/4034/ The goal of this minicourse is to review recent results in representation theory of finite-dimensional Lie superalgebras. Lecture 1 Finite-dimensional Lie superalgebras: classification, exam
From playlist Lie Theory and Representation Theory - 2015
Serganova, Vera, Lecture II - 22 January 2015
Vera Serganova (University of California, Berkeley) - Lecture II http://www.crm.sns.it/course/4034/ The goal of this minicourse is to review recent results in representation theory of finite-dimensional Lie superalgebras. Lecture 1 Finite-dimensional Lie superalgebras: classification, exa
From playlist Lie Theory and Representation Theory - 2015
Eigenvalues | Eigenvalues and Eigenvectors
In this video, we work through some example computations of eigenvalues of 2x2 matrices. Including a case where the eigenvalues are complex numbers. We do not discuss any intuition or definition of eigenvalues or eigenvectors, we simply carry out some elementary computations. If you liked
From playlist Linear Algebra
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
Vera Serganova: Capelli eigenvalue problem for Lie superalgebras and supersymetric polynominals
Abstract: We study invariant differential operators on representations of supergroups associated with simple Jordan superalgebras, in the classical case this problem goes back to Kostant. Eigenvalues of Capelli differential operators give interesting families of polynomials such as super J
From playlist Mathematical Physics
Minoru Wakimoto, Mock modular forms and representation theory of affine Lie superalgebras
Minoru WAKIMOTO (Université de Kyushu) "Mock modular forms and representation theory of affine Lie superalgebras - the case of sl(2|1)^"
From playlist Après-midi en l'honneur de Victor KAC
Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example
Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example A finite transformation is simply a lot of infinitesimal transformations! A Lie group, we have already show is a connected topological space and we know that any finite transformation can be built from a large product
From playlist Lie Groups and Lie Algebras
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
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
Eigenvectors of Symmetric Matrices Are Orthogonal
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
Definition of a Ring and Examples of Rings
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x
From playlist Abstract Algebra
This lecture is part of an online graduate course on Lie groups. We define the exponential map for matrix groups and describe its basic properties. (We also sketch two ways to define it for general Lie groups.) We give an example to show that it need not be surjective even for connected g
From playlist Lie groups
Nezhla Aghaei - Combinatorial Quantisation of Supergroup Chern-Simons Theory
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. In my talk, I will review the framework of combinatorial quantization of Chern Simons theory and
From playlist Workshop on Quantum Geometry
Alexey Bufetov: Representations of classical Lie groups: two growth regimes
Asymptotic representation theory deals with representations of groups of growing size. For classical Lie groups there are two distinguished regimes of growth. One of them is related to representations of infinite-dimensional groups, and the other appears in combinatorial and probabilistic
From playlist Probability and Statistics