arXiv subjects

Jacob Laubacher

Publications and source records attributed to Jacob Laubacher.

20 records · Page 2Linked to original sources

arXiv2017

Properties of the Secondary Hochschild Homology

In this paper we study properties of the secondary Hochschild homology of the triple $(A,B,\varepsilon)$ with coefficients in $M$. We establish a type of Morita equivalence between two triples and show that $H_\bullet((A,B,\varepsilon);M)$ is invariant under this equivalence. We also prove the existence of an exact sequence which connects the usual and the secondary Hochschild homologies in low dimension, allowing one to perform easy computations. The functoriality of $H_\bullet((A,B,\varepsilon);M)$ is also discussed.

math.RA↗

arXiv2016

Bar Simplicial Modules and Secondary Cyclic (Co)homology

In this paper we study the simplicial structure of the complex $C^{\bullet}((A,B,\varepsilon); M)$, associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object $\mathcal{B}(A,B,\varepsilon)$, which plays a role equivalent to that of the bar resolution associated to an algebra. We also introduce the secondary cyclic (co)homology and establish some of its properties (Theorems 3.9 and 4.11).

math.RA↗