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In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type. The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups.

In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type. The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups.

The classical groups form the deepest and most useful part of the subject of linear Lie groups. Most types of classical groups find application in classical and modern physics. A few examples are the following. The rotation group SO(3) is a symmetry of Euclidean space and all fundamental laws of physics, the Lorentz group O(3,1) is a symmetry group of spacetime of special relativity. The special unitary group SU(3) is the symmetry group of quantum chromodynamics and the symplectic group Sp(m) finds application in hamiltonian mechanics and quantum mechanical versions of it.

Particle Physics Topic 6: Lie Groups and Lie Algebras

Lecture from 2016 upper level undergraduate course in particle physics at Colorado School of Mines.

Lie groups and their Lie algebras - Lec 13 - Frederic Schuller

This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller.

Lie Groups and Lie Algebras | Lecture 2

The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI.

Mod-01 Lec-32 Continuous groups in physics (Part 1)

Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in.

Lec 11 | Lie Groups (Part 1)

Corollary 21.5 and equivariant form of Peter-Weyl theorem Section 22: characters and multiplicities Sections 26, 27: class functions and classical Fourier series.

Lec 5 | Lie Groups (Part 1)

Proof of Lemma 7.7: the Lie algebra of a Lie subgroup Section 9: closed subgroups Section 10: the groups SU(2) and SO(3) The references (section,corallary ...