Lie theory for symmetric Leibniz algebras

Abstract

Lie algebras and groups equipped with a multiplication \(\mu \) satisfying some compatibility properties are studied. These structures are called symmetric Lie \(\mu \)-algebras and symmetric \(\mu \)-groups respectively. An equivalence of categories between symmetric Lie \(\mu \)-algebras and symmetric Leibniz algebras is established when 2 is invertible in the base ring. The second main result of the paper is an equivalence of categories between simply connected symmetric Lie \(\mu \)-groups and finite dimensional symmetric Leibniz algebras.