This is a
glossary
A glossary (from , ''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. Traditionally, a gloss ...
for the terminology applied in the
mathematical
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
theories of
Lie groups
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Euclidean space, whereas ...
and
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...
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
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebra ...
.
Notations:
*Throughout the glossary,
denotes the
inner product
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, ofte ...
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
Claudio Procesi (born 31 March 1941 in Rome) is an Italian mathematician, known for works in algebra and representation theory.
Career
Procesi studied at the Sapienza University of Rome, where he received his degree (Laurea) in 1963. In 1966 he ...
(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 operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...
Wikipedia glossaries using description lists