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Article

Quadratic algebras arising from Hopf operads generated by a single element.

Letters in Mathematical Physics. 2020. Vol. 110. No. 8. P. 2053-2082.

The operads of Poisson and Gerstenhaber algebras are generated by a single binary element if we consider them as Hopf operads (i.e. as operads in the category of cocommutative coalgebras). In this note we discuss in detail Hopf operads generated by a single skew-symmetric element of arbitrary arity. We explain why the dual space to the space of n-ary operations in this operads are quadratic and Kozsul algebras. We give a detailed description of generators, relations and monominal bases in these algebras.