Internally connected graphs and the Kashiwara-Vergne Lie algebra

2016/12/09 by Felder, Matteo · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1612.03083

Abstract

It is conjectured that the Kashiwara-Vergne Lie algebra \widehat\mathfrakkrv₂ is isomorphic to the direct sum of the Grothendieck-Teichmüller Lie algebra \mathfrakgrt₁ and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of \widehat\mathfrakkrv₂ whose intersection is \mathfrakgrt₁, thus giving a way to interpolate between these two Lie algebras.

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