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Simplicial Structures Over the 3-Sphere and Generalized Higher Order Hochschild Homology

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arxiv 1707.03863 v2 pith:TUTKDCUN submitted 2017-07-12 math.AC math.KTmath.RA

Samuel Carolus , Jacob Laubacher This is my paper · ORCID
classification math.ACmath.KTmath.RA
keywords hochschildhomologysimplicialhigherordernaturalsphereassociated
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abstract

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.

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  1. Deformation Theories Controlled by Hochschild Cohomologies

    math.RA 2019-08 conditional novelty 4.0 of 10

    Higher-order Hochschild cohomology over any d-sphere and tertiary Hochschild cohomology control the associativity of deformed algebra products.

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