Poisson geometry and the Kashiwara-Vergne conjecture
英文摘要:
We give a Poisson-geometric proof of the Kashiwara-Vergne conjecture for quadratic Lie algebras, based on the equivariant Moser trick.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
A. Alekseev, E. Meinrenken
We give a Poisson-geometric proof of the Kashiwara-Vergne conjecture for quadratic Lie algebras, based on the equivariant Moser trick.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
This is a Bourbaki's seminar text. We introduce the combinatorial Kashiwara-Vergne conjecture on the Baker-Campbell-Hausdorff serie. After recalling previous results and consequences, we explain the Alekseev-Meinrenken's proof [math.QA/0506499]
We prove that a universal symmetric solution of the Kashiwara-Vergne conjecture is unique up to order one. in the Appendix by the second author, this result is used to show that solutions of the Kashiwara-Vergne conjecture for quadratic Lie algebras existing in the literature are not universal.
Consider the Kontsevich $\star$-product on the symmetric algebra of a finite dimensional Lie algebra $\mathfrak g$, regarded as the algebra of distributions with support 0 on $\mathfrak g$. In this paper, we extend this $\star$-product to distributions satisfying an appropriate support condition. As a consequence, we prove a long standing conjecture of Kashiwara-Vergne on the convolution of germs of invariant distributions on the Lie group $G$.
Let $G$ be a connected Lie group, with Lie algebra $g$. In 1977, Duflo constructed a homomorphism of $g$-modules $Duf: S(g) -> U(g)$, which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture on the Campbell-Hausdorff series, which (among other things) extends the Duflo theorem to germs of bi-invariant distributions on the Lie group $G$. The main results of the present paper are as follows. (1) Using a recent result of Torossian (2002), we establish the Kashiwara-Vergne conjecture for any Lie group $G$. (2) We give a reformulation of the Kashiwa…
This article follows our previous work on Campbell-Hausdorff formula. We study the case of symmetric spaces. We recover, by using a Kontsevich's deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the convolution of invariant distributions, for solvable symmetric spaces and "very symmetric spaces".
This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this preprint is due to the series of videotaped lectures (wClips) that are linked within.
The Kashiwara-Vergne (KV) conjecture is a property of the Campbell-Hausdorff series put forward in 1978. It has been settled in the positive by E. Meinrenken and the first author in 2006. In this paper, we study the uniqueness issue for the KV problem. To this end, we introduce a family of infinite dimensional groups KV_n, and an extension \hat{KV}_2 of the group KV_2. We show that the group \hat{KV}_2 contains the Grothendieck-Teichmueller group GRT as a subgroup, and that it acts freely and transitively on the set of solutions of the KV problem Sol(KV). Furthermore, we prove that Sol(KV) is …
We state a conjecture (due to M. Duflo) analogous to the Kashiwara--Vergne conjecture in the case of a characteristic $p>2$, where the role of the Campbell--Hausdorff series is played by the Jacobson element. We prove a simpler version of this conjecture using Vergne's explicit rational solution of the Kashiwara--Vergne problem. Our result is related to the structure of the Grothendieck--Teichmüller Lie algebra $\mathfrak{grt}$ in characteristic $p$: we conjecture existence of a generator of $\mathfrak{grt}$ in degree $p-1$, and we provide this generator for $p=3$ and $p=5$.
Finite Type Invariants of w-Knotted Objects II: Tangles, Foams and the Kashiwara-Vergne Problem
本文研究 w-缠结与 w-泡沫的有限型不变量,借箭头图将其联系于非有度 Lie 代数,并证明泛有限型不变量等价于 Kashiwara-Vergne 猜想的解。
In his work on crystal bases \cite{Kas}, Kashiwara introduced a certain degeneration of the quantized universal enveloping algebra of a semi-simple Lie algebra $\mathfrak g$, which he called a quantum boson algebra. In this paper, we construct Kashiwara operators associated to all positive roots and use them to define a variant of Kashiwara's quantum boson algebra. We show that a quasi-classical limit of the positive half of our variant is a Poisson algebra of the form $(P \simeq \mathbb C[\mathfrak n^{\ast}], \, \{~~,~~\}_P)$, where $\mathfrak n$ is the positive part of $\mathfrak g$ and $\{~…
In 1979, M. Kashiwara and M. Vergne formulated a conjecture on a Lie group G which implies that the Duflo isomorphism of Z(g) and S(g)^g extends to a natural module isomorphism between the spaces of germs of invariant distributions on G and g=Lie(G), respectively. They also proved their conjecture for G solvable. Using Kontsevich's deformation quantization we establish directly this result for distributions on any real Lie group G. In turn this gives a new proof of Duflo's result on the local solvability of bi-invariant differential operators on G.
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。