Gnedbaye, Allahtan Victor The \(k\)-ary algebras and their operads. (Les algèbres \(k\)-aires et leurs opérades.) (French. Abridged English version) Zbl 0837.17003 C. R. Acad. Sci., Paris, Sér. I 321, No. 2, 147-152 (1995). The author studies algebras with \((k + 1)\)-ary operations giving two generalizations of the notion of associativity. In analogy to the article by V. Ginzburg and M. Kapranov [Duke Math. J. 76, 203-272 (1994)], he defines and investigates \((k + 1)\)-ary quadratic operads. Also, he constructs a Hochschild homology theory for partially associative \((k + 1)\)-ary algebras \((k\) is odd) and joins the triviality of the homology of a free partially associative \((k + 1)\)-ary algebra with some properties of the corresponding operad. Reviewer: J.Kubarski (Łódź) Cited in 1 ReviewCited in 8 Documents MSC: 17A42 Other \(n\)-ary compositions \((n \ge 3)\) 18G99 Homological algebra in category theory, derived categories and functors Keywords:\(n\)-ary operation; \(n\)-ary composition; operads; Koszul duality; quadratic operads; Hochschild homology PDFBibTeX XMLCite \textit{A. V. Gnedbaye}, C. R. Acad. Sci., Paris, Sér. I 321, No. 2, 147--152 (1995; Zbl 0837.17003)