2008/03/04 by Nicolas Goze, Goze, Nicolas, Elisabeth Remm +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.0803.0553
23 pages
openalex publication_date 2008/03/04 · arxiv created 2008/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye's thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially associative algebras. First by reducing the space of cochains, secondly by using a graded version. Next we compute the free n-ary algebra, giving a basis of this algebra. At last we extend the notion of coalgebras to n-ary algebras.