Algebraic structures | Semigroup theory
In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse x, meaning that xax = x. The notion of weak inverse is (as the name suggests) weaker than the notion of inverse used in a regular semigroup (which requires that axa=a). The above definition of an E-inversive semigroup S is equivalent with any of the following: * for every element a ∈ S there exists another element b ∈ S such that ab is an idempotent. * for every element a ∈ S there exists another element c ∈ S such that ca is an idempotent. This explains the name of the notion as the set of idempotents of a semigroup S is typically denoted by E(S). The concept of E-inversive semigroup was introduced by in 1955. Some authors use E-dense to refer only to E-inversive semigroups in which the idempotents commute. More generally, a subsemigroup T of S is said dense in S if, for all x ∈ S, there exists y ∈ S such that both xy ∈ T and yx ∈ T. A semigroup with zero is said to be an E*-dense semigroup if every element other than the zero has at least one non-zero weak inverse. Semigroups in this class have also been called 0-inversive semigroups. (Wikipedia).
Inner & Outer Semidirect Products Derivation - Group Theory
Semidirect products are a very important tool for studying groups because they allow us to break a group into smaller components using normal subgroups and complements! Here we describe a derivation for the idea of semidirect products and an explanation of how the map into the automorphism
From playlist Group Theory
AlgTopReview4: Free abelian groups and non-commutative groups
Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such
From playlist Algebraic Topology
Group theory 7: Semidirect products
This is lecture 7 of an online course on group theory. It covers semidirect products and uses them to classify groups of order 6.
From playlist Group theory
Definition of the Symmetric Group
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Symmetric Group
From playlist Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Klein Four-Group is the smallest noncyclic abelian group. Every proper subgroup is cyclic. We look at the the multiplication in the Klein Four-Group and find all of it's subgroups.
From playlist Abstract Algebra
Jérémy Faupin : Scattering theory for Lindblad operators
Abstract: In this talk, I will consider a quantum particle interacting with a target. The target is supposed to be localized and the dynamics of the particle is supposed to be generated by a Lindbladian acting on the space of trace class operators. I will discuss scattering theory for such
From playlist Mathematical Physics
Abstract Algebra | Quotient Groups
We introduce the notion of a quotient group and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Amit Einav: Weak Poincaré inequalities in the absence of spectral gaps
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory Abstract: Weak Poincaré inequalities in the absence of spectral gaps Abstract: Poincaré inequality, which is probably best known for its applications in PDEs and calculus of variation, is one of
From playlist Workshop: Probabilistic and variational methods in kinetic theory
Abstract Algebra | The notion of a subgroup.
We present the definition of a subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Control of fluid motion by Mythily Ramaswamy
Program : Integrable systems in Mathematics, Condensed Matter and Statistical Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Denis Osin: Invariant random subgroups of acylindrically hyperbolic 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
57 Sundar - Invariant measures and ergodicity for stochastic Navier-Stokes equations
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Adam Skalski: Translation invariant noncommutative Dirichlet forms
Talk by Adam Skalski in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on April 28, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Abstract Algebra | Cosets of a subgroup.
We present the definition of a coset of a subgroup and give several examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - A.Gheondea
Aurelian Gheondea (Bilkent University, Ankara) / 11.09.17 Title: Symmetry versus Conservation Laws in Dynamical Quantum Systems: A Unifying Approach through Propagation of Fixed Points Abstract: We unify recent Noether type theorems on the equivalence of symmetries with conservation laws
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8
From playlist Dynamical Systems and Ordinary Differential Equations
Pascal Auscher: On representation for solutions of boundary value problems for elliptic systems (2)
In order to extend the first order approach to BVP with Lp data in the sense of Kenig-Pipher, we need to extend our semigroups to Lp setting. Unfortunately, our semigroups are seldom bounded on all of Lp. They turn out to be bounded on some abstract Hardy spaces associated to a first order
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
On the structure of quantum Markov semigroups - F. Fagnola - PRACQSYS 2018 - CEB T2 2018
Franco Fagnola (Department of Mathematics, Politecnico di Milano, Italy) / 06.07.2018 On the structure of quantum Markov semigroups We discuss the relationships between the decoherence-free subalgebra and the structure of the fixed point subalgebra of a quantum Markov semigroup on B(h) w
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
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
Vitaly Bergelson : Potpourri of open problems and conjectures in linear dynamics and ergodic theory
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 Dynamical Systems and Ordinary Differential Equations