Journal of Lie Theory· 2026Q2
On linearised and elliptic versions of the Kashiwara–Vergne Lie algebra
- 6citations
- Q2SCImago
- 2026year
Short summary
This paper introduces linearized (𝔩𝔨𝔯𝔳) and elliptic (𝔨𝔯𝔳 ell) versions of the Kashiwara–Vergne Lie algebra.
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Key points
- Introduces a linearized version (𝔩𝔨𝔯𝔳) of the Kashiwara–Vergne Lie algebra.
- Introduces an elliptic version (𝔨𝔯𝔳 ell) of the Kashiwara–Vergne Lie algebra.
- Relates the elliptic version 𝔨𝔯𝔳 ell to existing elliptic versions of the Grothendieck–Teichmüller (𝔤𝔯𝔱 ell) and double shuffle (𝔡𝔰 ell) Lie algebras.
- Discusses the relationships between the linearized and elliptic versions based on known Lie algebra connections.
AI-generated from the title and abstract; the full text is not read.
Abstract
The goal of this article is to define a linearized or depth-graded version 𝔩𝔨𝔯𝔳 , and a closely related elliptic version 𝔨𝔯𝔳 ell , of the Kashiwara–Vergne Lie algebra 𝔨𝔯𝔳 originally constructed by Alekseev and Torossian as the space of solutions to the linearized Kashiwara–Vergne problem. We show how the elliptic Lie algebra 𝔨𝔯𝔳 ell is related to earlier constructions of elliptic versions 𝔤𝔯𝔱 ell and 𝔡𝔰 ell of the Grothendieck–Teichmüller Lie algebra 𝔤𝔯𝔱 and the double shuffle Lie algebra 𝔡𝔰 respectively. Based on the known relationships between the three Lie algebra 𝔤𝔯𝔱 , 𝔡𝔰 and 𝔨𝔯𝔳 , we discuss the corresponding relationships between the linearized versions, and also between the elliptic versions.
The authors' abstract, as published at the source. Journal of Lie Theory, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics