规范变换诱导的Sh-李代数
Sh-Lie algebras Induced by Gauge Transformations
摘要：
"自旋$\leq 2$粒子“的物理学导致了场的矢量空间$Φ$上规范参数的李代数$Ξ$的表示。试图为自旋$>2$发展一个类似的理论已经失败了;事实上，有人声称这样一个理论是不可能的（尽管我们一直无法确定这样一个“行不通”定理的假设）。这导致BBvD [burgers：diss，BBvd：three，BBvD：probs]在一个可以用光滑函数进行分析的环境中推广到“场相关参数”。在认识到所得到的结构是sh-李代数（$L_\infty$ -代数）的结构之后，我们现在已经完全代数地再现了它们的结构，希望能对正在发生的事情有所启发。
英文摘要：
The physics of ``particles of spin $\leq 2$'' leads to representations of a Lie algebra $Ξ$ of gauge parameters on a vector space $Φ$ of fields. Attempts to develop an analogous theory for spin $>2$ have failed; in fact, there are claims that such a theory is impossible (though we have been unable to determine the hypotheses for such a `no-go' theorem). This led BBvD [burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent parameters' in a setting where some analysis in terms of smooth functions is possible. Having recognized the resulting structure as that of an sh-lie algebra ($L_\infty$-algebra), we have now reproduced their structure entirely algebraically, hopefully shedding some light on what is going on.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
