Loday 代数胚的上同调、非线性联络与示性类
Loday algebroids cohomology, nonlinear connections and characteristic classes
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中文总结 AI 辅助
本文通过引入作用 Loday 代数胚概念、明确其态射，研究 Loday 代数胚的非线性联络与示性类，建立广义 Chern-Simons 公式并定义其二阶示性类，推进了 Loday 代数胚的研究。
中文摘要 AI 辅助
本文旨在推进 Loday 代数胚的进一步研究，首先引入作用 Loday 代数胚的概念，明确 Loday 代数胚的（共）态射概念。随后聚焦于 Loday 代数胚的非线性联络及其相关示性类理论的研究，这些类源于 Loday 代数胚上同调中（关于 Loday 代数胚光滑截面模的）多重微分算子，特别考虑了 Loday 代数胚上非线性联络的 Chern-Simons 微分算子，建立了此类联络的广义 Chern-Simons 公式，并利用 Loday 代数胚的表示定义了其二阶示性类。
英文摘要
The purpose of this paper is to contribute to the further study of Loday algebroids by introducing, first, the concept of action Loday algebroid and clarifying the notion of a (co)morphism of Loday algebroids. We then focus on the study of Loday algebroids nonlinear connections and their related theory of characteristic classes. These classes arise from multidifferential operators (on the module of smooth sections of the Loday algebroid) in the Loday algebroid cohomology. In particular, the Chern-Simons differential operators for nonlinear connections on Loday algebroids are considered and a generalized Chern- Simons formula for such connections is established. Using representations of Loday algebroids, we define their secondary characteristic classes.
