Topological groups

Locally compact group

In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are locally compact and such groups have a natural measure called the Haar measure. This allows one to define integrals of Borel measurable functions on G so that standard analysis notions such as the Fourier transform and spaces can be generalized. Many of the results of finite group representation theory are proved by averaging over the group. For compact groups, modifications of these proofs yields similar results by averaging with respect to the normalized Haar integral. In the general locally compact setting, such techniques need not hold. The resulting theory is a central part of harmonic analysis. The representation theory for locally compact abelian groups is described by Pontryagin duality. (Wikipedia).

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Simple Groups - Abstract Algebra

Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order

From playlist Abstract Algebra

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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

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GT2. Definition of Subgroup

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

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The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication

From playlist Abstract Algebra

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The Special Linear Group is a Subgroup of the General Linear Group Proof

The Special Linear Group is a Subgroup of the General Linear Group Proof

From playlist Abstract Algebra

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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

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Teach Astronomy - Galaxy Groups

http://www.teachastronomy.com/ The typical cosmic environment for a galaxy is actually a group. A group can consist of more then two galaxies up to a few dozen galaxies. Usually there are a handful of large galaxies and a few dozen small galaxies or dwarfs because in any typical region o

From playlist 20. Galaxy Interaction and Motion

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Groups that commute Lesson 27

You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.

From playlist Abstract algebra

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Quotient groups

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

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Group Actions and Power Maps by C. R. E. Raja

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

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Proper Actions and Representation Theory Part 2

Professor Toshiyuki Kobayashi, University of Tokyo, Japan

From playlist Distinguished Visitors Lecture Series

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Proper Actions and Representation Theory Part 1

Professor Toshiyuki Kobayashi, University of Tokyo, Japan

From playlist Distinguished Visitors Lecture Series

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The orbit method for (certain) pro-p groups (Lecture 1) by Uri Onn

PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund

From playlist Group Algebras, Representations And Computation

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Sven Raum: Operator algebras of locally compact groups acting on trees

Sven Raum: Operator algebras of locally compact groups acting on trees Abstract: I will present my work on C*-simplicity of locally compact groups, focusing on its relevance for studying locally compact groups acting on trees. First, I will summarising results that I could obtain in 2015

From playlist HIM Lectures: Trimester Program "Von Neumann Algebras"

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Holomorphic Curves in Compact Quotients of SL(2,C) by Sorin Dumitrescu

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From playlist Topics in Hodge Theory - 2023

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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)

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Holomorphic rigid geometric structures on compact manifolds by Sorin Dumitrescu

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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Louis-Clément-Lefevre: Representation varieties of fundamental groups of complex algebraic...

We study locally the representation varieties of fundamental groups of smooth complex algebraic varieties. These are schemes whose complex points parametrize such representations into linear algebraic groups. At a given representation, the structure of the formal local ring to the represen

From playlist Topology

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Special Values of Zeta Functions (Lecture 1) by Matthias Flach

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

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Michael Wibmer: Etale difference algebraic 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 Algebraic and Complex Geometry

Related pages

Group representation | Lie group | Pontryagin duality | K-theory | Topological group | Topological vector space | Harmonic analysis | Discrete group | Algebraic K-theory | Rational number | Spectrum (topology) | Quotient group | Locally compact space | Hausdorff space | Finite group | Polish group | Mathematics | Equivalence of categories | Null set | Real number | Exact category | Compact group | Functor | Compact space | Integral | Prime number | Haar measure | Subgroup | Countable chain condition | Lp space | Measure (mathematics) | Normal space | P-adic number | Fourier transform | Borel measure | Abelian group | Closed set