Algebraic structures on parallelizable manifolds (Q6588212)

A manifold \(\mathbb{L}\) is parallelisable when its tangent bundle admits a global trivialisation. This defines a map \(\rho_p : \ell \to T_{p}\mathbb{L}\) for every \(p \in \mathbb{L}\). In this case, the flows of the fundamental vector fields give rise to a non-associative product between elements of \(\ell\) and \(\mathbb{L}\). The author describes these constructions and studies their properties. Moreover, he constructs a Lie algebra structure on \(\ell\), in a generalised sense.