2381/45955 Mamuka Jiblazde Mamuka Jiblazde Teimuraz Pirashvili Teimuraz Pirashvili Lie theory for symmetric Leibniz algebras University of Leicester 2019 Lie algebras Leibniz algebras Lie groups Algebraic theories 2019-10-18 08:58:40 Journal contribution https://figshare.le.ac.uk/articles/journal_contribution/Lie_theory_for_symmetric_Leibniz_algebras/10196090 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.