Properties of Higher Order Hochschild Cohomology
Date of Award
Doctor of Philosophy (Ph.D.)
Mihai Staic (Advisor)
Lianfeng Sun (Other)
Kit Chan (Committee Member)
Xiangdong Xie (Committee Member)
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.
Carolus, Samuel R., "Properties of Higher Order Hochschild Cohomology" (2019). Mathematics Ph.D. Dissertations. 41.