关于扬基类型代数和双泊松括弧的评论

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-04-01 DOI:10.1134/s0016266323040068

G. I. Olshanski, N. A. Safonkin

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引用次数: 0

摘要

摘要在最近的一篇论文中，其中一位作者提出了一种关联代数的构造，这种构造与 A 系列的扬基有许多共同的性质，但更庞大。我们的研究表明，这种构造可以推广，并揭示了它与自由关联代数上的双泊松括弧大家族的直接联系，后者由 Pichereau 和 Van de Weyer（2008 年）描述。

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Remarks on Yangian-Type Algebras and Double Poisson Brackets

Abstract

In a recent paper, one of the authors proposed a construction of associative algebras which share a number of properties of the Yangians of series A but are more massive. We show that this construction admits a generalization which reveals a direct connection with a large family of double Poisson brackets on free associative algebras, which was described by Pichereau and Van de Weyer (in 2008).

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.