Examples of Algebraic Operads
Identifieur interne : 000194 ( Main/Exploration ); précédent : 000193; suivant : 000195Examples of Algebraic Operads
Auteurs : Jean-Louis Loday [France] ; Bruno Vallette [France]Source :
- Grundlehren der mathematischen Wissenschaften [ 0072-7830 ] ; 2012.
Abstract
Abstract: In Chap. 9 , we studied in detail the operad Ass encoding the associative algebras. It is a paradigm for nonsymmetric operads, symmetric operads, cyclic operads. In this chapter we present several other examples of operads. First, we present the two other “graces”, the operads Com and Lie encoding respectively the commutative (meaning commutative and associative) algebras, and the Lie algebras. Second, we introduce more examples of binary quadratic operads: Poisson, Gerstenhaber, pre-Lie, Leibniz, Zinbiel, dendriform, magmatic, several variations like Jordan algebra, divided power algebra, Batalin–Vilkovisky algebra. Then we present various examples of operads involving higher ary-operations: homotopy algebras, infinite-magmatic, brace, multibrace, Jordan triples, Lie triples. The choice is dictated by their relevance in various parts of mathematics: differential geometry, noncommutative geometry, harmonic analysis, algebraic combinatorics, theoretical physics, computer science. Of course, this list does not exhaust the examples appearing in the existing literature. The reader may have a look at the cornucopia of types of algebras 2012 to find more examples.
Url:
DOI: 10.1007/978-3-642-30362-3_13
Affiliations:
- France
- Alsace (région administrative), Grand Est, Provence-Alpes-Côte d'Azur
- Nice, Strasbourg
- Université de Strasbourg
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Dieudonné, Université de Nice-Sophia Antipolis, Nice</wicri:regionArea><placeName><region type="region">Provence-Alpes-Côte d'Azur</region><region type="old region">Provence-Alpes-Côte d'Azur</region><settlement type="city">Nice</settlement></placeName></affiliation></author></analytic><monogr></monogr><series><title level="s">Grundlehren der mathematischen Wissenschaften</title><title level="s" type="sub">A Series of Comprehensive Studies in Mathematics</title><imprint><date>2012</date></imprint><idno type="ISSN">0072-7830</idno><idno type="ISSN">0072-7830</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0072-7830</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: In Chap. 9 , we studied in detail the operad Ass encoding the associative algebras. It is a paradigm for nonsymmetric operads, symmetric operads, cyclic operads. In this chapter we present several other examples of operads. First, we present the two other “graces”, the operads Com and Lie encoding respectively the commutative (meaning commutative and associative) algebras, and the Lie algebras. Second, we introduce more examples of binary quadratic operads: Poisson, Gerstenhaber, pre-Lie, Leibniz, Zinbiel, dendriform, magmatic, several variations like Jordan algebra, divided power algebra, Batalin–Vilkovisky algebra. Then we present various examples of operads involving higher ary-operations: homotopy algebras, infinite-magmatic, brace, multibrace, Jordan triples, Lie triples. The choice is dictated by their relevance in various parts of mathematics: differential geometry, noncommutative geometry, harmonic analysis, algebraic combinatorics, theoretical physics, computer science. Of course, this list does not exhaust the examples appearing in the existing literature. The reader may have a look at the cornucopia of types of algebras 2012 to find more examples.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Alsace (région administrative)</li><li>Grand Est</li><li>Provence-Alpes-Côte d'Azur</li></region><settlement><li>Nice</li><li>Strasbourg</li></settlement><orgName><li>Université de Strasbourg</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Loday, Jean Louis" sort="Loday, Jean Louis" uniqKey="Loday J" first="Jean-Louis" last="Loday">Jean-Louis Loday</name></region><name sortKey="Vallette, Bruno" sort="Vallette, Bruno" uniqKey="Vallette B" first="Bruno" last="Vallette">Bruno Vallette</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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