ZINBIEL ALGEBRAS AND COMMUTATIVE ALGEBRAS WITH DIVIDED POWERS

Abstract

AbstractIn this paper, we prove that any Zinbiel algebra can be endowed with the structure of commutative algebra with divided powers. We introduce the notion of universal enveloping Zinbiel algebra of a commutative algebra with divided powers algebras. We prove that the free divided powers algebra on a free module M, is the divided powers sub-algebra generated by M, of the divided powers algebra induced by the free Zinbiel algebra on M. Finally, we construct a basis for the enveloping Zinbiel algebra.