Lie theory for symmetric Leibniz algebras
journal contributionposted on 18.10.2019, 08:58 by Mamuka Jiblazde, Teimuraz Pirashvili
Lie algebras and groups equipped with a multiplication μ satisfying some compatibility properties are studied. These structures are called symmetric Lie μ -algebras and symmetric μ -groups respectively. An equivalence of categories between symmetric Lie μ -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 μ -groups and finite dimensional symmetric Leibniz algebras.