C*-algebras | Quantum groups | Functional analysis | Harmonic analysis | Representation theory

Locally compact quantum group

In mathematics and theoretical physics, a locally compact quantum group is a relatively new C*-algebraic approach toward quantum groups that generalizes the Kac algebra, compact-quantum-group and Hopf-algebra approaches. Earlier attempts at a unifying definition of quantum groups using, for example, multiplicative unitaries have enjoyed some success but have also encountered several technical problems. One of the main features distinguishing this new approach from its predecessors is the axiomatic existence of left and right invariant weights. This gives a noncommutative analogue of left and right Haar measures on a locally compact Hausdorff group. (Wikipedia).

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

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From playlist Abstract Algebra

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

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From playlist Abstract Algebra

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Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined

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From playlist Lie Groups and Lie Algebras

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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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STPM - The Cohomology of Arithmetic Groups - Simon Marshall

Simon Marshall Institute for Advanced Study September 27, 2010 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Benjamin Anderson-Sackaney - Tracial and G-invariant States on Quantum Groups

For a discrete group G, the tracial states on its reduced group $C^*$-algebra $C^∗_r (G)$ are exactly the conjugation invariant states. This makes the traces on $C^∗_r (G)$ amenable to group dynamical techniques. In the setting of a discrete quantum group ${\mathbb G}$, there is a quantum

From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”

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Gromov-Witten Theory and Gauge Theory (Lecture 2) by Constantin Teleman

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From playlist Vortex Moduli - 2023

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AlgTopReview4: Free abelian groups and non-commutative groups

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From playlist Algebraic Topology

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Symmetry in Quantum Gravity by Hirosi Ooguri

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From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

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Klaus Fredenhagen - Quantum Field Theory and Gravitation

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Victor Gayral: From equivariant quantization to locally compact quantum group ...

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An introduction to quantum chaos - Stéphane Nonnemacher

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From playlist Mathematics

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Symmetric groups

In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto

From playlist Abstract algebra

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Categorical aspects of vortices (Lecture 2) by Niklas Garner

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From playlist Vortex Moduli - 2023

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Quantum Theory - Full Documentary HD

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From playlist TV Appearances

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Yuri Kordyukov: Adiabatic limits and noncommutative geometry of foliations

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From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Rigorous RG: a provably efficient and possibly practical algorithm for... - Umesh Vazirani

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From playlist Mathematics

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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

Related pages

Quantum group | Coalgebra | Compact quantum group | Analytic continuation | Hopf algebra | Haar measure | Pontryagin duality | Mathematics | Locally compact field | Noncommutative geometry | Von Neumann algebra | Locally compact space | C*-algebra | Locally compact group