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1. Laubacher, Jacob C. Secondary Hochschild and Cyclic (Co)homologies.

Degree: PhD, Mathematics, 2017, Bowling Green State University

Hochschild cohomology was originally introduced in 1945. Much more recently in 2013 a generalization of this theory, the secondary Hochschild cohomology, was brought to light. In this dissertation we provide the details behind the simplicial structure for the chain complexes associated to the (secondary) Hochschild (co)homology. For this we introduce the notion of simplicial algebras and simplicial modules. The key results are two lemmas (3.4.1 and 3.4.2) that can be thought of as analogues of the Tor and Ext functors in the context of simplicial modules. It was a pleasant surprise that the higher order Hochschild homology over the 2-sphere can also be described using simplicial structures. We study some other related concepts like the secondary Hochschild and cyclic homologies associated to the triple (A,B,ε), as well as some of their properties. Advisors/Committee Members: Staic, Mihai D. (Advisor).

Subjects/Keywords: Mathematics; homological algebra; deformation theory; associative rings and algebras; Hochschild cohomology; cyclic cohomology

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APA (6th Edition):

Laubacher, J. C. (2017). Secondary Hochschild and Cyclic (Co)homologies. (Doctoral Dissertation). Bowling Green State University. Retrieved from

Chicago Manual of Style (16th Edition):

Laubacher, Jacob C. “Secondary Hochschild and Cyclic (Co)homologies.” 2017. Doctoral Dissertation, Bowling Green State University. Accessed October 27, 2020.

MLA Handbook (7th Edition):

Laubacher, Jacob C. “Secondary Hochschild and Cyclic (Co)homologies.” 2017. Web. 27 Oct 2020.


Laubacher JC. Secondary Hochschild and Cyclic (Co)homologies. [Internet] [Doctoral dissertation]. Bowling Green State University; 2017. [cited 2020 Oct 27]. Available from:

Council of Science Editors:

Laubacher JC. Secondary Hochschild and Cyclic (Co)homologies. [Doctoral Dissertation]. Bowling Green State University; 2017. Available from: