Divided power algebras over an operad
arXiv:1712.03694 · doi:10.1017/S0017089519000223
Abstract
The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We describe these polynomial operations in two different ways: one way uses invariant elements under the action of the symmetric group, the other coinvariant elements. Our results are then applied to the case of level algebras, which are (non-associative) commutative algebras satisfying the exchange law.
43 pages