Globalizations of partial group actions on non-associative algebras

This paper is a contribution to the globalization problem for partial group actions on non-associative algebras. We principally focus on partial group actions on Lie algebras, Jordan algebras and Malcev algebras. We give sufficient conditions for the existence and uniqueness of a globalization for partial group actions on the algebras already mentioned. As an application of this result, we show that in characteristic zero every partial group action on a semisimple Malcev algebra admits a globalization, unique up to isomorphism. We give a criterion for the existence and uniqueness of a globalization for a partial group action on a unital Jordan algebra in characteristic different from two, and on a sympathetic Lie algebra (a perfect Lie algebra without center and outer derivations).