Homotopy commutative algebra and 2-nilpotent Lie algebra

Michel Dubois-Violette (1) , Todor Popov (2)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 INRNE - Institute for Nuclear Research and Nuclear Energy

The homotopy transfer theorem due to Tornike Kadeishvili induces the structure of a homotopy commutative algebra, or $C_{\infty}$-algebra, on the cohomology of the free 2-nilpotent Lie algebra. The latter $C_{\infty}$-algebra is shown to be generated in degree one by the binary and the ternary operations.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Combinatoire [math.CO]; Algèbres quantiques [math.QA]

Michel Dubois-Violette, Todor Popov. Homotopy commutative algebra and 2-nilpotent Lie algebra. 2012. ⟨hal-00718938⟩