Geodesic
DIVIDED POWER ALGEBRAS OVER AN OPERAD
Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 477-517

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DOI

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 and 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. 
IKONICOFF, SACHA. DIVIDED POWER ALGEBRAS OVER AN OPERAD. Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 477-517. doi: 10.1017/S0017089519000223
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     title = {DIVIDED {POWER} {ALGEBRAS} {OVER} {AN} {OPERAD}},
     journal = {Glasgow mathematical journal},
     pages = {477--517},
     year = {2020},
     volume = {62},
     number = {3},
     doi = {10.1017/S0017089519000223},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000223/}
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