Glossary

Symbols

$A(n)$,
$C_0(X)$,
$\d_x$,
$E\otimes F$,
$\wh f$,
$\Gl(E)$,
$\Gl(n)$,
$\Hom(E,F)$,
$\Hom_G(\Psi,\Phi)$,
$\Hom_G(\Psi)$,
$L_2(G)$,
$M(G)$,
$M_b(G)$,
$M_1(G)$,
$\bar\Q$,
$\OO(n)$,
$P(\pi)$,
$\Q(\z)$,
$\R_1^{n+1}$,
$S^1$,
$S(n)$,
$\SO(n)$,
$\SU(n)$,
$T_xM$,
$\TT$,
$\UU(E)$,
$\UU(n)$,
$\bar\Z$,
$\la x,x^*\ra$,

A

abelianization,
adjacency matrix,
algebra,
algebraic integer,
algebraic number,
alternating group,
angular momentum operator,
angular momentum operator,
angular momentum quantum number,
annihilator,
approximate unit,
associative algebra,
atomic orbital,

B

Baker-Campell-Hausdorff formula,
baryon,
baryon number,
base of a root system
bi-invariant metric,
bipartite graph,

C

Cartan-algebra,
Cayley graph,
Cayley table,
center of a Lie-algebra,
centralizer,
character,
charge,
class function,
commutative Lie-algebra,
commutator,
commutator,
compact symplectic group,
companion matrix,
completely reducible representation,
complete vector field,
complex differentiable,
complexification,
complex structure,
compound character,
configuration space,
conjugacy class,
connected manifold,
contra-gredient representation,
center of a group,
contra-variant tensor,
convolution algebra,
coordinate-function,
coordinate transformation,
co-root,
covariant tensor,
critical,
cyclotomic field,

D

diagonalizable,
diffeomorphism,
dihedral group,
direct sum of representations,
Dirac operator,
dominant element
dual basis,
dual of a group,
dual representation,

E

eigen-frequency,
eigen-space,
eigen-state,
energy-momentum tensor field,
enveloping algebra,
equivalent algebra representations,
equivalent group representations,
Euler-Lagrange equations,
Euler-Lagrange field equation,
exchange operator,
exchange operator,

F

faithful representation,
finitely generated Abelian group,
first integral,
first quantum number,
flow of a vector field,
flow of a vector field,
Fourier coefficient,
Fourier transform,
fundamental weight system
fundamental Weyl chamber

G

generator,
generator of a one parameter group,
ground state,
group algebra,
group of symmetries,
group operation on a space,

H

Haar measure,
hadron,
Heisenberg group,
highest weight cyclic representation,
highest weight cyclic representation,
holomorphic,
homomorphism,
hypercharge,

I

ideal of an algebra,
improper rotation,
in-decomposable vector
induced character,
induced representation,
inner product,
integral element
intertwining operator,
invariant measure,
invariant sub-space,
irreducible representation,
irreducible representation,
irreducible sub-space,
isomorphic root system
isomorphism,
isospin,
isotypic component,

J

K

L

ladder operator,
Lagrange density,
Lagrangian,
left invariant vector field,
left-regular representation,
Lie-algebra,
linear group,
locally closed,
locally convex space,
Lorentz group,
Lorentz transformation,

M

magnetic quantum number,
matrix Lie-group,
mean value of an observable,
meson,
Minkowski space,
modular function,
multiplicity of an eigen-value,
multiplicity of a representation,
musical isomorphism,

N

nil-potent Lie-algebra,
non-singular form,
normal operator,
normalizer,
normalizer,

O

observable,
one-parameter group,
orbit,
orbit space,

P

partial trace,
partition,
partition function,
Pauli spin matrices,
polar,
positive linear operator,
probability current,
proper rotation,

Q

R

rank of a semi-simple Lie-algebra,
reducible root system
related vector fields,
representation,
representation of a Lie-algebra
root
root of a semi-simple Lie-algebra,
root system
root vector

S

SALC,
self-adjoint operator,
semi-simple Lie-algebra,
semi-simple Lie-algebra,
semi-simple operator,
simple algebra,
simple Lie-algebra,
simple eigen-value,
simply connected,
simultaneously diagonalizable,
site representation of a molecule,
skew symmetric operator,
solvable Lie-algebra,
special orthogonal group,
special unitary group,
spin addition,
spin exchange operator,
spin $l/2$ representation,
spherical harmonic,
square of angular momentum,
stabilizer,
stable state,
state,
strangeness
structure constants,
sub-manifold,
sub-representation,
symmetric group,
symplectic form,
symplectic group,
symplectic space,

T

tangent space,
tensor product of representations,
time-dependent Schrödinger equation,
topological group,
transitive action,
transposition,

U

unimodular,
unitary group,
unitary representation,
universal enveloping algebra,
universal property,

V

variance of an observable,
variation,
vector field,
vector field,
vector field,
Verma module,

W

weight,
weight,
weight space,
weight vector,
Weyl chamber
Weyl group of a semi-simple Lie-algebra,
Wirtinger operators,

X

Y

Z

Last modified: Thu Sep 1 11:06:37 CEST 2022