The idea of cyclic homology can be generalized to other skew-simplicial groups as shown by Krasauskas and independently by Fiodorowicz. The simplest analogue is the dihedral homology.
There is also a geometric analogy where
Hochschild homology is essentially the cohomology of free loop spaces;
cyclic homology is essentially the cohomology of free loop spaces modulo the circle group $SO(2)$ action by rotating on the loops;
so dihedral homology is the cohomology of free loop spaces modulo the $O(2)$-action on loops (including reflections, as in the dihedral group).
Last revised on March 5, 2023 at 17:57:11. See the history of this page for a list of all contributions to it.