This is a
glossary
A glossary (from grc, γλῶσσα, ''glossa''; language, speech, wording) also known as a vocabulary or clavis, is an alphabetical list of Term (language), terms in a particular domain of knowledge with the definitions for those terms. Tradi ...
for the terminology applied in the
mathematical theories of
Lie groups and
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
s. For the topics in the representation theory of Lie groups and Lie algebras, see
Glossary of representation theory
This is a glossary of representation theory in mathematics.
The term "module" is often used synonymously for a representation; for the module-theoretic terminology, see also glossary of module theory.
See also Glossary of Lie groups and Lie alg ...
. Because of the lack of other options, the glossary also includes some generalizations such as
quantum group.
Notations:
*Throughout the glossary,
denotes the
inner product of a Euclidean space ''E'' and
denotes the rescaled inner product
::
A
B
C
D
E
F
G
H
I
J
K
L
N
M
P
Q
R
S
Classical Lie algebras:
Exceptional Lie algebras:
T
U
*
Unitarian trick
V
*
Verma module
W
References
*
*
Erdmann, Karin & Wildon, Mark. ''Introduction to Lie Algebras'', 1st edition, Springer, 2006.
* Humphreys, James E. ''Introduction to Lie Algebras and Representation Theory'', Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York, 1978.
*
Jacobson, Nathan, ''Lie algebras'', Republication of the 1962 original. Dover Publications, Inc., New York, 1979.
*
*
Claudio Procesi (2007) ''Lie Groups: an approach through invariants and representation'', Springer, .
*.
*J.-P. Serre, "Lie algebras and Lie groups", Benjamin (1965) (Translated from French)
{{DEFAULTSORT:Glossary Of Lie Algebras
Lie Algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
Wikipedia glossaries using description lists