Mathematics Ph.D. Dissertations

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.

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