5 papers
Replacing bar-like resolutions in a simplicial setting
Samuel Carolus, Jacob Laubacher, Sydney D. Vitalbo +1
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. Thi…
Deformation Theories Controlled by Hochschild Cohomologies
Samuel Carolus, Samuel A. Hokamp, Jacob Laubacher
We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the -sphere for any $d\g…
A Simplicial Construction for Noncommutative Settings
Samuel Carolus, Jacob Laubacher, Mihai D. Staic
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 co…
-Algebra Structure on the Higher Order Hochschild Cohomology
Samuel Carolus, Mihai D. Staic
We present a deformation theory associated to the higher Hochschild cohomology . We also study a -algebra structure associated to this deformation theory.
Simplicial Structures Over the 3-Sphere and Generalized Higher Order Hochschild Homology
Samuel Carolus, Jacob Laubacher
In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the -sphere. We also introduce the tertiary Hoch…