Operads of decorated trees and their duals

Vsevolod Yu. Gubarev; Pavel S. Kolesnikov

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 4, page 421-445
  • ISSN: 0010-2628

Abstract

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This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform splitting. However, our approach is more algebraic and thus provides simpler way to prove various properties of pre- and post-algebras in general.

How to cite

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Gubarev, Vsevolod Yu., and Kolesnikov, Pavel S.. "Operads of decorated trees and their duals." Commentationes Mathematicae Universitatis Carolinae 55.4 (2014): 421-445. <http://eudml.org/doc/261995>.

@article{Gubarev2014,
abstract = {This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform splitting. However, our approach is more algebraic and thus provides simpler way to prove various properties of pre- and post-algebras in general.},
author = {Gubarev, Vsevolod Yu., Kolesnikov, Pavel S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Leibniz algebra; dialgebra; dendriform algebra; pre-Lie algebra; Leibniz algebra; dialgebra; dendriform algebra; pre-Lie algebra},
language = {eng},
number = {4},
pages = {421-445},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Operads of decorated trees and their duals},
url = {http://eudml.org/doc/261995},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Gubarev, Vsevolod Yu.
AU - Kolesnikov, Pavel S.
TI - Operads of decorated trees and their duals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 4
SP - 421
EP - 445
AB - This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform splitting. However, our approach is more algebraic and thus provides simpler way to prove various properties of pre- and post-algebras in general.
LA - eng
KW - Leibniz algebra; dialgebra; dendriform algebra; pre-Lie algebra; Leibniz algebra; dialgebra; dendriform algebra; pre-Lie algebra
UR - http://eudml.org/doc/261995
ER -

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