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.

中文翻译：

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对称莱布尼兹代数的李理论

研究了配备有满足一些相容性的乘法\（\ mu \）的李代数和群。这些结构分别称为对称Lie \（\ mu \）-代数和对称\（\ mu \） -组。当基环中的2是可逆的时，对称的Lie \（\ mu \）代数和对称的Leibniz代数之间的类别相等。本文的第二个主要结果是简单连接的对称Lie \（\ mu \） -群和有限维对称Leibniz代数之间的类别等价。