论文标题
光谱分区的操作在代数和TAQ协同学
Operations on spectral partition Lie algebras and TAQ cohomology
论文作者
论文摘要
我们确定了所有自然操作及其在光谱分区的同质群体上的关系，该组件与$ \ mthbb {f} _p $ -linear-linear-linear topologicalandré-Quillen共同体学在任何素数中都相吻合。我们在光谱分区的同型组群上构建一单位作战，并在代数的同型群体组上构建了限制性的谎言代数结构。然后，我们证明了一份单一操作的组成法，以及一单位操作与移动的谎言括号之间的兼容条件，并限制到一个单位进行限制。与Brantner-Mathew在自由光谱分区的同型组中的结果相比，我们推断出这些产生所有自然操作，从而在$ \ Mathbb {f} _p $ linelear taq taq共同体学上恢复了Kriz和Basterra-Mandell的未公开结果。作为推论，我们确定了mod $ p $ $ \ mathbb {s} $ - 线性taq共同体的自然操作结构。
We determine all natural operations and their relations on the homotopy groups of spectral partition Lie algebras, which coincide with $\mathbb{F}_p$-linear topological André-Quillen cohomology operations at any prime. We construct unary operations and a shifted restricted Lie algebra structure on the homotopy groups of spectral partition Lie algebras. Then we prove a composition law for the unary operations, as well as a compatibility condition between unary operations and the shifted Lie bracket with restriction up to a unit for the restriction. Comparing with Brantner-Mathew's result on the ranks of the homotopy groups of free spectral partition Lie algebras, we deduce that these generate all natural operations, thereby also recovering unpublished results of Kriz and Basterra-Mandell on $\mathbb{F}_p$-linear TAQ cohomology operations. As a corollary, we determine the structure of natural operations on mod $p$ $\mathbb{S}$-linear TAQ cohomology.
