Invitation to composition. (English) Zbl 0948.18004
A “composition system” is a pre-operad (or “non-symmetric operad”), i.e., a graded module \(C\) with partial compositions
\[
\circ_i\: C^m\otimes C^n\to C^{m+n-1}, \qquad 0\leq i\leq m-1
\]
satisfying certain composition and unitality conditions. M. Gerstenhaber [Ann. Math., II. Ser. 78, 267-288 (1963; Zbl 0131.27302)] uncovered such a structure in the Hochschild complex of an associative algebra. As in the Hochschild complex, a cup product, a graded Lie-algebra, a “pre-coboundary operator”, and several other structures can be associated to a pre-operad. A “derivation deviation” of the pre-coboundary operator is calculated in two ways.
Reviewer: Bjørn Dundas (Trondheim)
MSC:
| 18D50 | Operads (MSC2010) |
Keywords:
(pre-)operads; Gerstenhaber theory; composition; derivation deviation; precoboundary operatorCitations:
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