Linear Lie algebras

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A linear (or "classical") Lie algebras is a Lie algebra whose elements can be represented as matrices (or linear transformations over some vector space over a field.

A-series[edit | edit source]

Root system[edit | edit source]

Realisation[edit | edit source]

See also: sl(n) (special linear Lie algebra)

An A-series Lie algebra is realised by the ring of n-by-n traceless matrices.

C-series[edit | edit source]

B-series[edit | edit source]

D-series[edit | edit source]

Notes[edit | edit source]

  • James E. Humphreys (1972), Introduction to Lie Algebras and Representation Theory, Springer-Verlag, ISBN 9780387900537