A concept of $\frac23$PROP and deformation theory of (co)associative bialgebras

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dc.creatorShoikhet, Boris
dc.date2003-11-19
dc.date.accessioned2026-07-07T05:03:03Z
dc.date.available2026-07-07T05:03:03Z
dc.descriptionWe introduce a concept of $\frac23$PROP generalizing the Kontsevich concept of $\frac12$PROP. We prove that some Stasheff-type compactification of the Kontsevich spaces $K(m,n)$ defines a topological $\frac23$PROP structure. The corresponding chain complex is a minimal model for its cohomology (both are considered as $\frac23$PROPs). We construct a $\frac23$PROP $\End(V)$ for a vector space $V$. Finally, we construct a dg Lie algebra controlling the deformations of a (co)associative bialgebra. Philosophically, this construction is a version of the Markl's operadic construction from [M1] applied to minimal models of $\frac23$PROPs.
dc.descriptionDedicated to Borya Feigin in the occasion of his 50th birthday 17 pages, 5eps figures, latex
dc.identifierhttps://arxiv.org/abs/math/0311337
dc.identifierhttp://arxiv.org/abs/math/0311337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69262
dc.subjectQuantum Algebra
dc.subjectK-Theory and Homology
dc.titleA concept of $\frac23$PROP and deformation theory of (co)associative bialgebras
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