The CROCs, non-commutative deformations, and (co)associative bialgebras

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dc.creatorShoikhet, Boris
dc.date2003-06-09
dc.date.accessioned2026-07-07T04:58:41Z
dc.date.available2026-07-07T04:58:41Z
dc.descriptionWe compactify the spaces $K(m,n)$ introduced by Maxim Kontsevich. The initial idea was to construct an $L_\infty$ algebra governing the deformations of a (co)associative bialgebra. However, this compactification leads not to a resolution of the PROP of (co)associative bialgebras, but to a new algebraic structure we call here a CROC. It turns out that these constructions are related to the non-commutative deformations of (co)associative bialgebras. We construct an associative dg algebra conjecturally governing the non-commutative deformations of a bialgebra. Then, using the Quillen duality, we construct a dg Lie algebra conjecturally governing the commutative (usual) deformations of a (co)associative bialgebra. Philosophically, the main point is that for the associative bialgebras the non-commutative deformations is maybe a more fundamental object than the usual commutative ones.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0306143
dc.identifierhttp://arxiv.org/abs/math/0306143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67738
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectK-Theory and Homology
dc.titleThe CROCs, non-commutative deformations, and (co)associative bialgebras
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