Computability theory | Semigroup theory

Automatic semigroup

In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines "canonical forms" for the elements of the semigroup, the other languages determine if two canonical forms represent elements that differ by multiplication by a generator. Formally, let be a semigroup and be a finite set of generators. Then an automatic structure for with respect to consists of a regular language over such that every element of has at least one representative in and such that for each , the relation consisting of pairs with is regular, viewed as a subset of (A# × A#)*. Here A# is A augmented with a padding symbol. The concept of an automatic semigroup was generalized from automatic groups by Campbell et al. (2001) Unlike automatic groups (see Epstein et al. 1992), a semigroup may have an automatic structure with respect to one generating set, but not with respect to another. However, if an automatic semigroup has an identity, then it has an automatic structure with respect to any generating set (Duncan et al. 1999). (Wikipedia).

Video thumbnail

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

Video thumbnail

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"

Video thumbnail

Group automorphisms in abstract algebra

Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem

From playlist Abstract algebra

Video thumbnail

GT14. Semidirect Products

EDIT: At 6:24, the product should be "(e sub H, e sub N)", not "(e sub H, e sub G)" Abstract Algebra: Using automorphisms, we define the semidirect product of two groups. We prove the group property and construct various examples, including the dihedral groups. As an application, we

From playlist Abstract Algebra

Video thumbnail

Inner Semidirect Product Example: Dihedral Group

Semidirect products explanation: https://youtu.be/Pat5Qsmrdaw Semidirect products are very useful in group theory. To understand why, it's helpful to see an example. Here we show how to write the dihedral group D_2n as a semidirect product, and how we can describe that purely using cyclic

From playlist Group Theory

Video thumbnail

SHM - 16/12/2016 - The algebraic theory of semigroups (...) - Christopher HOLLINGS

Mathématiques aux États-Unis dans la première moitié du XXe siècle et leurs relations avec l'Europe (séance préparée par Simon Decaens) Christopher Hollings (Oxford University) : "The algebraic theory of semigroups: interactions between US and European mathematics during the 20th century"

From playlist Séminaire d'Histoire des Mathématiques

Video thumbnail

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

Video thumbnail

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

Video thumbnail

The potential of AI, illustrated in the classification of finite..(Lecture 5) by Carlos Simpson

INFOSYS-ICTS RAMANUJAN LECTURES EXPLORING MODULI SPEAKER: Carlos Simpson (Université Nice-Sophia Antipolis, France) DATE: 10 February 2020 to 14 February 2020 VENUE: Madhava Lecture Hall, ICTS Campus Lecture 1: Exploring Moduli: basic constructions and examples 4 PM, 10 February 2020

From playlist Infosys-ICTS Ramanujan Lectures

Video thumbnail

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

Video thumbnail

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

Video thumbnail

Charles Batty: Rates of decay associated with operator semigroups

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

Video thumbnail

Introduction to Number Theory

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist Computer - Cryptography and Network Security

Video thumbnail

Peter Sarnak: Hyperbolic equations and spectral geometry

Programme for the Abel Lectures 2005: 1. "Abstract Phragmen-Lindelöf theorem & Saint Venant’s principle" by Abel Laureate 2005 Peter D. Lax, New York University 2. "Systems of conservation laws" by Professor Sebastian Noelle, CMA Oslo/ RWTH Aachen 3. "Hyperbolic equations and spectra

From playlist Abel Lectures

Video thumbnail

"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

Video thumbnail

Homomorphisms in abstract algebra

In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu

From playlist Abstract algebra

Video thumbnail

Jean Bourgain - 1/2 The orbital circle method and applications...

Jean Bourgain - The orbital circle method and applications / Toral eigenfuctions and their nodal sets

From playlist École d'été 2014 - Théorie analytique des nombres

Video thumbnail

Definition of a group Lesson 24

In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el

From playlist Abstract algebra

Video thumbnail

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

Video thumbnail

Semigroups and Abelian Algebraic Structures

Thesis: https://www.researchgate.net/publication/328163392_The_Cayley_type_theorem_for_semigroups Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Paper's Playlist: https://www.youtube.com/watch?v=nvYqkhZFzyY&lis

From playlist Bachelor's Paper

Related pages

Word problem for groups | Automatic group | Mathematics | Semigroup | Group (mathematics)