Dialgebras and Related Operads

J.-L. Loday, A. Frabetti, F. Chapoton, F. Goichot (Autoren)

Buch | Softcover

VIII, 140 Seiten

2001 | 2001
Springer Berlin (Verlag)
978-3-540-42194-8 (ISBN)

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four The of this volume deal with new notions of whose papers algebras feature is common to have two So are called generating operations. they dial- bras. The first motivation to introduce such structures a algebraic was problem in It turned out later that some of them dendriform algebraic K-theory. (the related are to in the of ren- dialgebras) closely Hopf algebras occuring theory malization of A. Connes and D. Kreimer. are also related to the They closely notion of Gerstenhaber homotopy algebra. Let us first describe the motivation from The algebraic K-theory. al- braic of a are not like the but K-groups ring periodic topological K-groups, of of some them shows the existence of a computation periodicity phenomenon. For instance the 0 are of 4 for 2. The groups K,,(Z) Q periodic period n are constructed on the linear GL. If algebraic K-groups general we - group it its additive that is the Lie then the place by counterpart, algebra gl, analogue of is : it is denoted HC. It algebraic K-theory computable cyclic homology, turns that for out this the is well understood. theory periodicity phenomenon It takes the form of a exact : long sequence - - - -+ -.+ -4 HCn_1 HH,,, -+ HC,, --+ HCn-2 HCn+1 where HHstands for Hochschild In other homology. words, cyclic homology is not but the obstruction to is it is periodic (in general) periodicity known, Hochschild homology.

Dialgebras.- Dialgebra (co)homology with coefficients.- Un endofoncteur de la catégorie des opérades.- Un théoréme de Milnor-Moore pour les algèbres de Leibniz.

Erscheint lt. Verlag	17.7.2001
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 140 p.
Verlagsort	Berlin
Sprache	englisch
Gewicht	218 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • dualgebras • Homology • Hopf Algebras • Koszul duality • operads • planar trees
ISBN-10	3-540-42194-7 / 3540421947
ISBN-13	978-3-540-42194-8 / 9783540421948
Zustand	Neuware