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DIVIDED POWER ALGEBRAS OVER AN OPERAD

Part of: Categories with structure General nonassociative rings

Published online by Cambridge University Press:  27 May 2019

SACHA IKONICOFF
SACHA IKONICOFF*
Affiliation:
Univ Paris Diderot, Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS, Sorbonne Université, 8 place Aurélie Nemours, F-75013 Paris, France e-mail: sacha.ikonicoff@imj-prg.fr
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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 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.

MSC classification

Primary: 18D50: Operads
Secondary: 17A30: Algebras satisfying other identities
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 477 - 517
Copyright
© Glasgow Mathematical Journal Trust 2019

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