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The generalized $${\mathcal A}_{\infty}$$-algebra structure on BGG sequences and generalized associative operad. (English) Zbl 1051.18006
Bureš, Jarolím (ed.), The proceedings of the 22nd winter school “Geometry and physics”, Srní, Czech Republic, January 12–19, 2002. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 71, 163-183 (2003).
The author discusses the structure of a generalized $$\mathcal{A}_\infty$$-algebra on the set of pieces of Bernstein-Gelfand-Gelfand (BGG) sequences. An explicit form of higher operations (pentagon relation) of this generalized $$\mathcal{A}_\infty$$-algebra is computed. Then, it is shown that these generalized $$\mathcal{A}_\infty$$-algebras are algebras over a certain operad.
For the entire collection see [Zbl 1014.00011].
##### MSC:
 18D50 Operads (MSC2010) 55U05 Abstract complexes in algebraic topology