Lie groups with commuting and anticommuting parameters

In this paper we study analogs of Lie algebras and formal Lie groups. These analogs of groups differ from usual Lie groups, roughly speaking, in that they admit anticommuting canonical parameters. The analogs of Lie algebras differ from usual Lie algebras by properties of the commutator. In the definition of these objects an essential role is played by the gradient. In case it is trivial they become Lie groups and algebras in the usual sense. To these generalized objects we carry over classical theorems on the connection between Lie groups and algebras and the basic representation theory.
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