李超代数𝔤𝔩m|n的双延代数和反射代数

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2024-04-13 DOI:10.1142/s021919972450007x

Lucia Bagnoli, Slaven Kožić

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引用次数: 0

摘要

我们研究了与李超代数𝔤𝔩m|n相关的双杨式。我们的主要重点是建立双杨式的波恩卡莱-伯克霍夫-维特定理，并以量子收缩系数的形式构造其中心元。接下来，作为一个应用，我们引入了反射代数，即 0 级双扬格的某些左协元子代数，并通过生成器和关系找到了它们的呈现形式。

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Double Yangian and reflection algebras of the Lie superalgebra 𝔤𝔩m|n

We study the double Yangian associated with the Lie superalgebra ${𝔤 𝔩}_{m | n}$ . Our main focus is on establishing the Poincaré–Birkhoff–Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations.

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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.