arXiv subjects

Samuel Carolus

Publications and source records attributed to Samuel Carolus.

5 recordsLinked to original sources

arXiv2024

Replacing bar-like resolutions in a simplicial setting

It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. This is, in fact, a feature of its construction via derived functors. For generalizations and extensions of the Hochschild (co)homology, one uses a bar-like resolution in a simplicial setting in order to accommodate the changing module structures in every dimension. In this note, we present a method in order to replace these bar-like resolutions.

math.RA↗

arXiv2019

Deformation Theories Controlled by Hochschild Cohomologies

We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the $d$-sphere for any $d\geq1$, we also investigate a deformation theory corresponding to the tertiary Hochschild cohomology, which naturally reduces to those studied for the secondary and usual Hochschild cohomologies under certain conditions.

math.RA↗

arXiv2019

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

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 $(A,B,C,\varepsilon,θ)$, 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.

math.AC↗

arXiv2019

A Simplicial Construction for Noncommutative Settings

In this paper we present a general construction that can be used to define the higher Hochschild homology for a noncommutative algebra. We also discuss other examples where this construction can be used.

math.RA↗

arXiv2018

$G$-Algebra Structure on the Higher Order Hochschild Cohomology $H^*_{S^2}(A,A)$

We present a deformation theory associated to the higher Hochschild cohomology $H_{S^2}^*(A,A)$. We also study a $G$-algebra structure associated to this deformation theory.

math.RA↗