In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of internal symmetries, but also contains some fermionic supercharges, transforming as a sum of N real spinor representations of the Poincaré group. Such symmetries are allowed by the Haag–Łopuszański–Sohnius theorem. When N>1 the algebra is said to have extended supersymmetry. The supersymmetry algebra is a semidirect sum of a central extension of the super-Poincaré algebra by a compact Lie algebra B of internal symmetries. Bosonic fields commute while fermionic fields anticommute. In order to have a transformation that relates the two kinds of fields, the introduction of a Z2-grading under which the even elements are bosonic and the odd elements are fermionic is required. Such an algebra is called a Lie superalgebra. Just as one can have representations of a Lie algebra, one can also have representations of a Lie superalgebra, called supermultiplets. For each Lie algebra, there exists an associated Lie group which is connected and simply connected, unique up to isomorphism, and the representations of the algebra can be extended to create group representations. In the same way, representations of a Lie superalgebra can sometimes be extended into representations of a Lie supergroup. (Wikipedia).
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra
Vector subspaces, their bases and dimensions -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
The determinant -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
Lattice Supersymmetric Field Theories (Lecture 1) by David Schaich
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
Seiberg-Witten Theory, Part 1 - Edward Witten
Seiberg-Witten Theory, Part 1 Edward Witten Institute for Advanced Study July 19, 2010
From playlist PiTP 2010
The magic of matrix multiplication | Linear Algebra MATH1141 | N J Wildberger
We prove the crucial result that matrix multiplication is associative. Along the way we review summation notation and get practice with indices and ranges. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise over
From playlist Higher Linear Algebra
Units in a Ring (Abstract Algebra)
The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar
From playlist Abstract Algebra
Supersymmetry: Some Reflections on the Future of a Symmetry from the Future - 4 dicembre 2019
https://www.sns.it/it/evento/supersymmetry-some-reflections-on-the-future-of-symmetry-from-the-future Colloqui della Classe di Scienze Supersymmetry: Some Reflections on the Future of a Symmetry from the Future Segio Ferrara (CERN) 2019 Special Breakthrough Prize in Fundamental Physics “
From playlist Colloqui della Classe di Scienze
Bootstrapping the space of 4d N=2 SCFTs by Madalena Lemos
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Supersymmetry and Superspace, Part 2 - Jon Bagger
Supersymmetry and Superspace, Part 2 Jon Bagger Johns Hopkins University July 20, 2010
From playlist PiTP 2010
Algebra - Ch. 4: Exponents & Scientific Notation (1 of 35) What is an Exponent?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an exponent. A number or symbol placed above another number or symbol that indicates the power the number or symbol at the bottom is raised. The number at the bottom is called the base
From playlist ALGEBRA CH 4 EXPONENTS AND SCIENTIFIC NOTATION
Lattice Supersymmetry - I by Simon Catterall
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Supersymmetry and Superspace, Part 1 - Jon Bagger
Supersymmetry and Superspace, Part 1 Jon Bagger Johns Hopkins University July 19, 2010
From playlist PiTP 2010
Session 2 - Bootstrapping Theories with Four Supercharge: Sheer El-Showk
https://strings2015.icts.res.in/talkTitles.php
From playlist Strings 2015 conference