Algebraic structures | Semigroup theory
In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of distinct nonisomorphic semigroups with one element is one. If S = { a } is a semigroup with one element, then the Cayley table of S is The only element in S is the zero element 0 of S and is also the identity element 1 of S. However not all semigroup theorists consider the unique element in a semigroup with one element as the zero element of the semigroup. They define zero elements only in semigroups having at least two elements. In spite of its extreme triviality, the semigroup with one element is important in many situations. It is the starting point for understanding the structure of semigroups. It serves as a counterexample in illuminating many situations. For example, the semigroup with one element is the only semigroup in which 0 = 1, that is, the zero element and the identity element are equal. Further, if S is a semigroup with one element, the semigroup obtained by adjoining an identity element to S is isomorphic to the semigroup obtained by adjoining a zero element to S. The semigroup with one element is also a group. In the language of category theory, any semigroup with one element is a terminal object in the category of semigroups. (Wikipedia).
Walter van Suijlekom: Semigroup of inner perturbations in Non Commutative Geometry
Starting with an algebra, we define a semigroup which extends the group of invertible elements in that algebra. As we will explain, this semigroup describes inner perturbations of noncommutative manifolds, and has applications to gauge theories in physics. We will present some elementary e
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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
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
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
The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Before we carry on with our coset journey, we need to discover when the left- and right cosets are equal to each other. The obvious situation is when our group is Abelian. The other situation is when the subgroup is a normal subgroup. In this video I show you what a normal subgroup is a
From playlist Abstract algebra
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
Definition of the Symmetric Group
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Symmetric Group
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
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
An asymptotic for the growth of Markoff-Hurwitz tuples - Ryan Ronan
Special Seminar Topic: An asymptotic for the growth of Markoff-Hurwitz tuples Speaker: Ryan Ronan Affiliation: Baruch College, The City University of New York Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
CEB T2 2017 - Fraydoun Rezakhanlou - 3/3
Fraydoun Rezakhanlou (Berkeley) - 09/06/2017 The lectures will discuss the following topics: 1. Scalar Conservation Laws and theirs Markovian solutions 2. Conservation laws with stochastic external force 3. Hamilton-Jacobi PDE, Hamiltonian ODEs and Mather Theory 4. Homogenization for
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
BAG1.4. Toric Varieties 4 - Spec(R) and Affine Semigroups
Basic Algebraic Geometry: In this part, we introduce Spec(R) and affine semigroups. This allows us to give yet another characterization of affine toric varieties in terms of affine semigroups.
From playlist Basic Algebraic Geometry
"New Paradigms in Invariant Theory" - Roger Howe, Yale University [2011]
HKUST Institute for Advanced Study Distinguished Lecture New Paradigms in Invariant Theory Speaker: Prof Roger Howe, Yale University Date: 13/6/2011 Video taken from: http://video.ust.hk/Watch.aspx?Video=6A41D5F6B1A790DC
From playlist Mathematics
Fraydoun Rezakhanlou: Homogenizations for Hamilton-Jacobi PDEs and Hamiltonian ODEs
Traditionally homogenization asks whether average behavior can be discerned from Hamilton-Jacobi equations that are subject to high-frequency fluctuations in spatial variables. A similar question can be asked for the associated Hamiltonian ODEs. When the Hamiltonian function
From playlist Probability and Statistics
Abstract Algebra | Cyclic Subgroups
We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Terry Lyons: Modelling Diffusive Systems
This lecture was held at The University of Oslo, May 24, 2007 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2007 1. “A Short History of Large Deviations” by Srinivasa Varadhan, Abel Laureate 2007, Courant
From playlist Abel Lectures
34 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
Zero dimensional valuations on equicharacteristic (...) - B. Teissier - Workshop 2 - CEB T1 2018
Bernard Teissier (IMJ-PRG) / 06.03.2018 Zero dimensional valuations on equicharacteristic noetherian local domains. A study of those valuations based, in the case where the domain is complete, on the relations between the elements of a minimal system of generators of the value semigroup o
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
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