Linear Lie algebras
From Wikiversity - Reading time: 1 min
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
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