Double Shuffle and Kashiwara-Vergne Lie algebras

2012/01/25 by Schneps, Leila · 4 citations
#17B37 #17B45 #17B70 #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1201.5316

Abstract

We prove that the double shuffle Lie algebra ds, dual to the space of new formal multiple zeta values, injects into the Kashiwara-Vergne Lie algebra krv defined and studied by Alekseev-Torossian. The proof is based on a reformulation of the definition of krv, and uses a theorem of Ecalle on a property of elements of ds.

Cited by

• A Lie algebra associated with adjoint multiple zeta values
• Ecalle's senary relation and dimorphic structures
• Reduced coaction Lie algebra, double shuffle Lie algebra and noncommutative krv2 equation
• Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures

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