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On realizations of the Steenrod algebras
Alexei Lebedev and Dimitry A. Leites
The Steenrod algebra can not be realized as an enveloping of any Lie superalgebra. We list several problems that suggest a need to modify the definition of the enveloping algebra, for example, to get rid of certain strange deformations which we qualify as an artifact of the inadequate definition of the enveloping algebra in positive characteristic. P.Deligne appended our paper with a realization the Steenrod algebra as a supergroup scheme, his comments, hints and open problems.