泊松几何中的经典 KMS 函数和相变

Pub Date : 2024-06-03 DOI:10.4310/jsg.2023.v21.n5.a3

Nicolò,Drago, Stefan,Waldmann

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引用次数: 0

摘要

在本文中，我们在泊松几何的背景下研究了满足经典 KMS 条件的不一定光滑度量的凸锥。与韦恩斯坦在光滑情况下的开创性工作类似，我们讨论了 KMS 度量的一般性质及其与底层泊松几何的关系。此外，通过归纳交映情况下的结果，我们将重点放在 $b$- 泊松流形的情况下，在这种情况下，我们提供了 KMS 度量凸锥的几乎完整特征。

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Classical KMS functionals and phase transitions in Poisson geometry

In this paper we study the convex cone of not necessarily smooth measures satisfying the classical KMS condition within the context of Poisson geometry. We discuss the general properties of KMS measures and their relation with the underlying Poisson geometry in analogy to Weinstein’s seminal work in the smooth case. Moreover, by generalizing results from the symplectic case, we focus on the case of $b$-Poisson manifolds, where we provide an almost complete characterization of the convex cone of KMS measures.

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