乔丹代数的矩图

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2024-05-04 DOI:10.1142/s0219199724500159

Claudio Gorodski, Iryna Kashuba, María Eugenia Martin

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引用次数: 0

摘要

我们利用几何不变论的技术研究了复杂 n 维乔丹代数的种类。更具体地说，我们利用基尔万-内斯（Kirwan-Ness）定理，就与经典矩映射相关的能量函数而言，将乔丹数的种类构造成有限多个不变局部封闭子集的莫尔斯型分层。特别是，我们在乔丹代数的背景下，获得了半简单乔丹代数众所周知的刚性的无同调新证明。

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A moment map for the variety of Jordan algebras

We study the variety of complex $n$ -dimensional Jordan algebras using techniques from Geometric Invariant Theory. More specifically, we use the Kirwan–Ness theorem to construct a Morse-type stratification of the variety of Jordan algebras into finitely many invariant locally closed subsets, with respect to the energy functional associated to the canonical moment map. In particular we obtain a new, cohomology-free proof of the well-known rigidity of semisimple Jordan algebras in the context of the variety of Jordan algebras.

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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.