论文标题
量规代数和遗产学 - 奎林 - 蒂奇定理的连续共同学
Continuous cohomology of gauge algebras and bornological Loday-Quillen-Tsygan theorems
论文作者
论文摘要
我们研究了众所周知的Loday-Quillen-Tsygan定理，该定理计算了一般线性代数$ \ Mathfrak {gl}（a）$的谎言代数同源性。对于Fréchet空间，这等于连续的代数同源性。为此，我们准备了有关拓扑矢量空间的同源代数的几个陈述，并讨论伯恩学杂志和环状复合物的差异何时是fréchet代数的拓扑同构。我们将结果应用于平滑函数的代数上，并在欧几里得空间上的平滑歧管和紧凑的平滑功能上应用，并从局部到全球原理构造了类似gelfand-fuks的光谱序列，该频谱序列计算了非trifigi虫级代数的稳定部分的稳定部分。这补充了Maier，Janssens和Wockel。
We investigate the well-known Loday-Quillen-Tsygan theorem, which calculates the Lie algebra homology of the general linear algebra $\mathfrak{gl}(A)$ for an associative algebra $A$ in terms of cyclic homology, and extend the proof to bornological Lie algebra homology of Fréchet and LF-algebras. For Fréchet spaces, this equals continuous Lie algebra homology. To this end we prepare several statements about homological algebra of topological vector spaces, and discuss when the differential of the bornological Hochschild and cyclic complex are topological homomorphisms in the setting of Fréchet algebras. We apply the results to the algebras of smooth functions on a smooth manifold and compactly supported smooth functions on Euclidean space, and construct from a local-to-global principle a Gelfand-Fuks-like spectral sequence which calculates the stable part of bornological Lie algebra homology of nontrivial gauge algebras. This complements results by Maier, Janssens and Wockel.
