Mathematics Ph.D. Dissertations
Title
Properties of Higher Order Hochschild Cohomology
Date of Award
2019
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Mathematics/Mathematics (Pure)
First Advisor
Mihai Staic (Advisor)
Second Advisor
Lianfeng Sun (Other)
Third Advisor
Kit Chan (Committee Member)
Fourth Advisor
Xiangdong Xie (Committee Member)
Abstract
In this dissertation, we show that HS2 *(A; A), the higher order Hochschild cohomology over S2, has a G-algebra structure. We also offer an explicit description of a chain complex to compute higher order Hochschild homology over S3. We then use the resulting three-dimensional picture to define a new generalization of Hochschild homology called the ternary Hochschild homology. Finally, we offer a way to define higher order homology over S2 when the algebra is noncommutative.
Recommended Citation
Carolus, Samuel R., "Properties of Higher Order Hochschild Cohomology" (2019). Mathematics Ph.D. Dissertations. 41.
https://scholarworks.bgsu.edu/math_diss/41