- In mathematics, the
complexification of a
vector space V over the
field of real
numbers (a "real
vector space")
yields a
vector space VC over the complex...
- In mathematics, the
complexification or
universal complexification of a real Lie
group is
given by a
continuous homomorphism of the
group into a complex...
-
algebra g0 is
called a real form of a
complex Lie
algebra g if g is the
complexification of g0: g ≃ g 0 ⊗ R C . {\displaystyle {\mathfrak {g}}\simeq {\mathfrak...
- {\displaystyle {\mathfrak {sl}}(2,\mathbb {C} )} is
isomorphic to the
complexification of s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} ,
meaning the tensor...
- mutation.
Complexification: the
ability of the
system (including
evolutionary algorithm and
genotype to
phenotype mapping) to
allow complexification of the...
- Jv)+i\omega (u,v).}
Given any real
vector space V we may
define its
complexification by
extension of scalars: V C = V ⊗ R C . {\displaystyle V^{\mathbb...
- {\displaystyle E} can be
promoted to a
complex vector bundle, the
complexification E ⊗ C ; {\displaystyle E\otimes \mathbb {C} ;}
whose fibers are E x...
-
exactly the same as the
definition bar the
field change. Sp(n, C) is the
complexification of the real
group Sp(2n, R). Sp(2n, R) is a real, non-compact, connected...
-
using Weyl's
unitary trick: each
semisimple real Lie
group G has a
complexification,
which is a
complex Lie
group Gc, and this
complex Lie
group has a...
-
smallest real form of a
corresponding complex Lie algebra,
namely the
complexification. Formally, one may
define a
compact Lie
algebra either as the Lie algebra...
