Dialgebras and Related Operads: 1763 (Lecture Notes in Mathematics, 1763) - Softcover

Loday, J.-L.; Frabetti, A.; Chapoton, F.; Goichot, F.

Softcover

ISBN 10: 3540421947 ISBN 13: 9783540421948

Publisher: Springer, 2001

Synopsis

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.

About this title

Product Description

The main object of study of these four papers is the notion of associative dialgebras which are algebras equipped with two associative operations satisfying some more relations of the associative type. This notion is studied from a) the homological point of view: construction of the (co)homology theory with trivial coefficients and general coefficients, b) the operadic point of view: determination of the dual operad, that is the dendriform dialgebras which are strongly related with the planar binary trees, c) the algebraic point of view: Hopf structure and Milnor-Moore type theorem.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 3540421947
• ISBN 13: 9783540421948
• Binding: Paperback
• Number of pages: 148