What does quantum group mean?

Definitions for quantum group
quan·tum group

Here are all the possible meanings and translations of the word quantum group.

Wikipedia

  1. Quantum group

    In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a "bicrossproduct" class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.

Freebase

  1. Quantum group

    In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects. The term "quantum group" often denotes a kind of noncommutative algebra with additional structure that first appeared in the theory of quantum integrable systems, and which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.

CrunchBase

  1. Quantum Group

    The Quantum Group provides electronic communication systems for hospitals, doctors, and patients to optimize the efficiency of healthcare institutions.

Editors Contribution

  1. quantum group

    A group of people come together, plan logistics, careful thinking in a balanced manner, achieve desired goal, collective thinking, action, calculations, precision.

    Submitted by anonymous on May 16, 2020  

How to pronounce quantum group?

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How to say quantum group in sign language?

  1. quantumgroup

Numerology

  1. Chaldean Numerology

    The numerical value of quantum group in Chaldean Numerology is: 8

  2. Pythagorean Numerology

    The numerical value of quantum group in Pythagorean Numerology is: 4

Images & Illustrations of quantum group

  1. quantum group


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"quantum group." Definitions.net. STANDS4 LLC, 2020. Web. 26 May 2020. <https://www.definitions.net/definition/quantum+group>.

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