In mathematics, if φ: G→H is a homomorphism of Lie groups, and g and h are the Lie algebras of G and H respectively, then the induced map φ* on tangent spaces is a homomorphism of Lie algebras, i.e. satisfies
Equivalently, such a representation may be described as a bilinear map (x,v)→x.v from g×V to V satisfying the Jacobi identity analogue
See also representations of Lie groups.