共查询到20条相似文献,搜索用时 15 毫秒
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Carlo A. Rossi 《Comptes Rendus Mathematique》2012,350(19-20):871-874
We give a different proof of the famous result on compatibility between cup product (Kontsevich, 2003, [3, Section 8]) in cohomology of degree 0, for a finite-dimensional Lie algebra, from which we deduce an alternative way of re-writing Kontsevich?s star product by means of the Alekseev–Torossian connection (Alekseev and Torossian, 2010, [1]). 相似文献
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We show that the Kashiwara–Vergne (KV) problem for quadratic Lie algebras (that is, Lie algebras admitting an invariant scalar product) reduces to the problem of representing the Campbell–Hausdorff series in the form , where and are Lie series in x and y. This observation explains the existence of explicit rational solutions of the quadratic KV problem, whereas constructing an explicit rational solution of the full KV problem would probably require the knowledge of a rational Drinfeld associator. It also gives, in the case of quadratic Lie algebras, a direct proof of the Duflo theorem (implied by the KV problem). To cite this article: A. Alekseev, C. Torossian, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
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Anton Alekseev Nariya Kawazumi Yusuke Kuno Florian Naef 《Comptes Rendus Mathematique》2017,355(2):123-127
We define a family of Kashiwara–Vergne problems associated with compact connected oriented 2-manifolds of genus g with boundary components. The problem is the classical Kashiwara–Vergne problem from Lie theory. We show the existence of solutions to for arbitrary g and n. The key point is the solution to based on the results by B. Enriquez on elliptic associators. Our construction is motivated by applications to the formality problem for the Goldman–Turaev Lie bialgebra . In more detail, we show that every solution to induces a Lie bialgebra isomorphism between and its associated graded . For , a similar result was obtained by G. Massuyeau using the Kontsevich integral. For , , our results imply that the obstruction to surjectivity of the Johnson homomorphism provided by the Turaev cobracket is equivalent to the Enomoto–Satoh obstruction. 相似文献
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Seung-Jo Jung 《Journal of Pure and Applied Algebra》2018,222(7):1579-1605
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The Kashiwara–Vergne (KV) conjecture states the existence of solutions of a pair of equations related with the Campbell–Baker–Hausdorff
series. It was solved by Meinrenken and the first author over ℝ, and in a formal version, by two of the authors over a field
of characteristic 0. In this paper, we give a simple and explicit formula for a map from the set of Drinfeld associators to
the set of solutions of the formal KV equations. Both sets are torsors under the actions of prounipotent groups, and we show
that this map is a morphism of torsors. When specialized to the KZ associator, our construction yields a solution over ℝ of
the original KV conjecture. 相似文献
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Peter Jossen 《Inventiones Mathematicae》2014,195(2):393-439
We show that the statement analogous to the Mumford–Tate conjecture for Abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associated Hodge group and the unipotent part of the image of the absolute Galois group with the unipotent part of the motivic fundamental group. 相似文献
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The Ramanujan Journal - We extend the author’s earlier computation and give coefficient formulas for the (quasimodular) Poincaré square series of weight 3 / 2 and... 相似文献
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Yong-Gao Chen 《Comptes Rendus Mathematique》2012,350(21-22):933-935
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In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of d-th syzygy of R-modules of finite length, provided R is an isolated singularity. Based on this result, it is shown that under a mild assumption on the base ring R, satisfying the Auslander–Reiten conjecture behaves well under completion and reduction modulo regular elements. In addition, it will turn out that, if R is a commutative Noetherian ring and 𝒬 a finite acyclic quiver, then the Auslander–Reiten conjecture holds true for the path algebra R𝒬, whenever so does R. Using this result, examples of algebras satisfying the Auslander–Reiten conjecture are presented. 相似文献
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Zhifu You 《Discrete Applied Mathematics》2009,157(8):1766-1772
The Randi? index of a graph G is defined as , where d(u) is the degree of vertex u and the summation goes over all pairs of adjacent vertices u, v. A conjecture on R(G) for connected graph G is as follows: R(G)≥r(G)−1, where r(G) denotes the radius of G. We proved that the conjecture is true for biregular graphs, connected graphs with order n≤10 and tricyclic graphs. 相似文献
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Wei Zhang 《The Ramanujan Journal》2012,29(1-3):225-256
We obtain a relative Shalika germ expansion of orbital integrals appeared in the relative trace formulae Jacquet?CRallis when n=3. This is the first example where there are infinitely many nilpotent orbits. As an application we can prove the smooth transfer conjecture of Jacquet?CRallis for n=3. 相似文献
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Let $\kappa \ge 6$ be an even integer, $M$ an odd square-free integer, and $f \in S_{2\kappa -2}(\Gamma _0(M))$ a newform. We prove that under some reasonable assumptions that half of the $\lambda $ -part of the Bloch–Kato conjecture for the near central critical value $L(\kappa ,f)$ is true. We do this by bounding the $\ell $ -valuation of the order of the appropriate Bloch–Kato Selmer group below by the $\ell $ -valuation of algebraic part of $L(\kappa ,f)$ . We prove this by constructing a congruence between the Saito–Kurokawa lift of $f$ and a cuspidal Siegel modular form. 相似文献
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We give equivalent formulations of the Erd?s-Turán conjecture on the unboundedness of the number of representations of the natural numbers by additive bases of order two of . These formulations allow for a quantitative exploration of the conjecture. They are expressed through some functions of reflecting the behavior of bases up to x. We examine some properties of these functions and give numerical results showing that the maximum number of representations by any basis is ?6. 相似文献