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arXiv · 1712.03694

Divided power algebras over an operad

Sacha Ikonicoff
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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.

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Sacha Ikonicoff. 2017-12-11. Divided power algebras over an operad. https://doi.org/10.1017/s0017089519000223

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