The Koszul complex is the cotangent complex

Actually, we check in Section 5 that for nilpotent Lie algebras over a field of characteristic zero, up to dimension 9 the reduced Koszul map is always zero (by reduction to

— After a review of definitions and some properties of protoperads (see [Ler19]) in Section 1, following the results on properads (see [Val03, Val07, MV09a]), we introduce the notion

pre-symplectic structure η, and prove that its Maurer-Cartan equation encodes the deformations of η inside the space of pre-symplectic structures of fixed rank.. We located the

Using an operad of graph complexes we prove, with the help of an earlier result of one of the authors [W3], that there is a highly non-trivial action of the Grothendieck-Teichm¨

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To study algebraic structures defined by operations with multiple inputs and multiple outputs, like bialgebras or Lie bialgebras for instance, one needs to generalize the notion

This paper develops the Koszul duality theory for protoperads, defined in [Ler18], which are an analog of properads (see [Val03, Val07]) with more less symmetries.. The main

We have seen above that the Chevalley-Eilenberg complex of L (with homological grading) is a resolution of A, and the Chevalley-Eilenberg complexes of L ≥2 and L ≥3 calculate