By Dikran Dikranjan, Luigi Salce

ISBN-10: 0585322007

ISBN-13: 9780585322001

ISBN-10: 0824719379

ISBN-13: 9780824719371

Contains a stimulating collection of papers on abelian teams, commutative and noncommutative jewelry and their modules, and topological teams. Investigates at present well known themes similar to Butler teams and nearly thoroughly decomposable teams.

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**Sample text**

Let (C, O) be a symmetric monoidal category with internal Hom functor, Hom,,. The endomorphism operad £ndx for an object X E C is defined by Sndx(n) := Hom^(X°n,X). F Mn) is defined by 7n;mi, ,m+,(o,,/B1,... (D /3n) The right E, action on £ndx (n) is defined by composition with the left Enaction on X°n induced by the symmetric monoidal structure on C. The operad £ndx is particularly important because the theory of operads was developed as a tool in understanding algebraic or topological structures involving a sequence of n-ary operations on an object of a symmetric monoidal category.

Other examples of n-ary algebras are introduced in [Gne96]. 13. 8, a dg operad P is itself a monoid in a symmetric monoidal category, the bar construction expressed in the appropriate generality applies to P, producing a dg cooperad 13(P). 1. We will also need the dual dg operad D(P), which is just C(P) suitably regraded. The operads C(P) and D(P) were introduced by Ginzburg and Kapranov in [GK94] while the operad 13(P) was introduced by Getzler and Jones in [GJ94). If Ass is the operad for associative algebras, then D(Ass) is the operad Ass.

Map from HH* (A; A) to CH* (A; A), thus exhibiting the higher order terms in the deformation. ) Cattaneo and Felder [CF99] have given a E-model derivation of Kontsevich's quantization; it relates to the 'Swiss-cheese' operad of Voronov [Vor98]. Since operads themselves can be regarded as generalized algebras, it is not hard to define `formality' for dg operads [Mar96c]: DEFINITION. A dg operad P is formal if there is a dg operad X with dg operad morphisms P - X -> H(P) which induce isomorphisms in homology.

### Abelian groups, module theory, and topology: proceedings in honor of Adalberto Orsatti's 60th birthday by Dikran Dikranjan, Luigi Salce

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