C*-algebras | Quantum groups | Hopf algebras
In mathematics, a compact quantum group is an abstract structure on a unital separable C*-algebra axiomatized from those that exist on the commutative C*-algebra of "continuous complex-valued functions" on a compact quantum group. The basic motivation for this theory comes from the following analogy. The space of complex-valued functions on a compact Hausdorff topological space forms a commutative C*-algebra. On the other hand, by the Gelfand Theorem, a commutative C*-algebra is isomorphic to the C*-algebra of continuous complex-valued functions on a compact Hausdorff topological space, and the topological space is uniquely determined by the C*-algebra up to homeomorphism. S. L. Woronowicz introduced the important concept of compact matrix quantum groups, which he initially called compact pseudogroups. Compact matrix quantum groups are abstract structures on which the "continuous functions" on the structure are given by elements of a C*-algebra. The geometry of a compact matrix quantum group is a special case of a noncommutative geometry. (Wikipedia).
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
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The Special Linear Group is a Subgroup of the General Linear Group Proof
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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
Definition of the Symmetric Group
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Symmetric Group
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Quantum Mechanics 1.1: Introduction
In this video I provide some motivation behind the development of quantum mechanics, kicking off a new series on everything you've been wondering about quantum mechanics! Twitter: https://twitter.com/SciencePlease_
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Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
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Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/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
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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
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Arthur Troupel - Free Wreath Products as Fundamental Graph C*-algebras
The free wreath product of a compact quantum group by the quantum permutation group S+N has been introduced by Bichon in order to give a quantum counterpart of the classical wreath product. The representation theory of such groups is well-known, but some results about their operator algebr
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Ernesto Lupercio: On the moduli space for Quantum Toric Varieties
Talk by Ernesto Lupercio in Global Noncommutative Geometry Seminar (Americas) on November 5, 2021, https://globalncgseminar.org/talks/tba-17/
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David Kyed: The Podleś spheres converge to the sphere
Talk by David Kyed in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on June 16, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
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Jens Kaad: Exterior products of compact quantum metric spaces
Talk by Jens Kaad in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 24, 2020.
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Gromov-Witten Theory and Gauge Theory (Lecture 2) by Constantin Teleman
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Karen Strung: Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
Talk by Karen Strung in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 12, 2021
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Protein Collapse and Folding by Govardhan Reddy
Indian Statistical Physics Community Meeting 2016 URL: https://www.icts.res.in/discussion_meeting/details/31/ DATES Friday 12 Feb, 2016 - Sunday 14 Feb, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community wh
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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
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