On realizations of the Steenrod algebras

Abstract

The Steenrod algebra can not be realized as an enveloping of any Lie superalgebra. We list several problems that suggest a need to mod- ify the definition of the enveloping algebra, for example, to get rid of cer- tain 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 his comments, hints and open problems.