持久模的张量、对称、外幂和其他幂
Tensor, Symmetric, Exterior, and Other Powers of Persistence Modules
摘要：
我们重新制定的持续（上）的同源性的单纯过滤，从一个更代数的设置，即作为（上）的同源性的链复形的分次模多项式环$K[t]$。定义了群、结合代数、李代数等的持久（余）同调。然后给出了张量幂\par的计算公式，其中$M$是持久模。我们讨论了持久模的循环幂和二面体幂，更一般地讨论了$T^n(M)$的群作用的幂。
英文摘要：
We reformulate the persistent (co)homology of simplicial filtrations, viewed from a more algebraic setting, namely as the (co)homology of a chain complex of graded modules over polynomial ring $K[t]$. We also define persistent (co)homology of groups, associative algebras, Lie algebras, etc. \par Then we obtain formulas for tensor powers $T^n(M),S^n(M),Λ^{\!n}(M)$ where $M$ is a persistence module. We discuss the cyclic and dihedral powers of persistence modules, and more generally quotients of $T^n(M)$ by a group action.
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。
