%0 Journal Article
%T Simplicial structures over the 3-sphere and generalized higher order Hochschild homology
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Carolus, Samuel
%A Laubacher, Jacob
%D 2021
%\ 07/01/2021
%V 15
%N 1
%P 93-143
%! Simplicial structures over the 3-sphere and generalized higher order Hochschild homology
%K Higher order Hochschild homology
%K pre-simplicial algebras
%K deformations
%R 10.52547/cgasa.15.1.93
%X In this paper, we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the $3$-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple $(A,B,C,\varepsilon,\theta)$, which becomes natural after we organize the elements in a convenient manner. We establish these results by way of a bar-like resolution in the context of simplicial modules. Finally, we generalize the higher order Hochschild homology over a trio of simplicial sets, which also grants natural geometric realizations.
%U https://cgasa.sbu.ac.ir/article_101063_6bc0541f88d6be98b33e6ef64d0f04c1.pdf