### 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

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

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

Quantum Group

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

### Editors Contribution

quantum group

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### Numerology

Chaldean Numerology

The numerical value of quantum group in Chaldean Numerology is:

**8**Pythagorean Numerology

The numerical value of quantum group in Pythagorean Numerology is:

**4**

## Translations for **quantum group**

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- مجموعة الكمArabic

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