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...

mutation. Complexification: the ability of the system (including evolutionary algorithm and genotype to phenotype mapping) to allow complexification of the...

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...

infinity in the complex projective plane that are contained in the complexification of every real circle. A point of the complex projective plane may be...

its complexification is a simple complex Lie algebra, unless L is already the complexification of a Lie algebra, in which case the complexification of...

{\displaystyle {\mathfrak {sl}}(2,\mathbb {C} )} is isomorphic to the complexification of s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} , meaning the tensor...

finite-dimensional real Lie algebra is semisimple if and only if its complexification is semisimple. Each endomorphism x of a finite-dimensional vector space...

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...

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...