Classical Lie algebras

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The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types , , and , where for the general linear Lie algebra and the identity matrix:

  • , the special linear Lie algebra;
  • , the odd-dimensional orthogonal Lie algebra;
  • , the symplectic Lie algebra; and
  • , the even-dimensional orthogonal Lie algebra.

Except for the low-dimensional cases and , the classical Lie algebras are simple.[1][2]

The Moyal algebra is an infinite-dimensional Lie algebra that contains all classical Lie algebras as subalgebras.

See alsoEdit


  1. ^ Antonino., Sciarrino,; Paul., Sorba, (2000-01-01). Dictionary on Lie algebras and superalgebras. Academic Press. ISBN 9780122653407. OCLC 468609320.CS1 maint: extra punctuation (link)
  2. ^ 1945–, Sthanumoorthy, Neelacanta,. Introduction to finite and infinite dimensional lie (super)algebras. ISBN 9780128046753. OCLC 952065417.CS1 maint: extra punctuation (link) CS1 maint: numeric names: authors list (link)