Thomas Willwacher
The cubical complex of a permutation group representation - or however you want to call it.
Fri, 03/18/2011 - 16:01 — SomNambulAuthors: Pavol Severa, Thomas Willwacher
Subjects: Quantum Algebra
AbstractThis paper is about a small combinatorial trick, which is well known, but has
no name. Let G be a permutation group acting on a vector space M. There is a
natural way to assign a cosimplicial space to these data. We call the resulting
cochain complex the cubical complex. Its cohomology is easy to compute. We give
some examples of its occurrence in nature.- 13 comments
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M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra.
Fri, 09/10/2010 - 15:01 — SomNambulAuthors: Thomas Willwacher
Subjects: Quantum Algebra
AbstractWe show that the zeroth cohomology of Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichm\"uller Lie algebra grt. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. Also, it allows proving the freeness part of the
Deligne-Drinfeld conjecture in some low orders. As a side result one obtains
that the homotopy deformations of the Gerstenhaber operad are parameterized by
grt. Finally, our methods give a second proof of a result of H.A note on the Koszul complex in deformation quantization.
Mon, 02/15/2010 - 16:01 — SomNambulAuthors: Andrea Ferrario, Carlo A. Rossi, Thomas Willwacher
Subjects: Quantum Algebra
AbstractThe aim of this short note is to present a proof of Conjecture 1.3 of
\cite{CFFR} about the existence of an $A_\infty$-quasi-isomorphism between the
$A_\infty$-$\mathrm S(V^*)$-$\wedge(V)$-bimodule $K$, introduced in
\cite{CFFR}, and the Koszul complex $\mathrm K(V)$ of $\mathrm S(V^*)$, viewed
as a $\mathrm S(V^*)$-$\wedge(V)$-bimodule, for $V$ a finite-dimensional
(complex or real) vector space.
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