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Coalgebraic Approach to the Loday Infinity Category, Stem Differential for $2 n$ -ary Graded and Homotopy Algebras

Mourad Ammar; Norbert Poncin — 2010

Annales de l’institut Fourier

We define a graded twisted-coassociative coproduct on the tensor algebra the desuspension space of a graded vector space $V$ . The coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1-to-1 with sequences of multilinear maps on $V$ (resp. graded Loday structures on $V$ , sequences that we call Loday infinity structures on $V$ ). We prove a minimal model theorem for Loday infinity algebras and observe that the ${Lod}_{\infty}$ category contains the $L_{\infty}$ category as...

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Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2 n -ary Graded and Homotopy Algebras

Coalgebraic Approach to the Loday Infinity Category, Stem Differential for $2 n$ -ary Graded and Homotopy Algebras