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Secondary Hochschild and Cyclic (Co)homologies

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2017, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics.
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.
Mihai D. Staic, Ph.D. (Advisor)
John Laird, Ph.D. (Other)
Xiangdong Xie, Ph.D. (Committee Member)
Juan Bes, Ph.D. (Committee Member)
160 p.

Recommended Citations

Citations

  • Laubacher, J. C. (2017). Secondary Hochschild and Cyclic (Co)homologies [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1489422065908758

    APA Style (7th edition)

  • Laubacher, Jacob. Secondary Hochschild and Cyclic (Co)homologies. 2017. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1489422065908758.

    MLA Style (8th edition)

  • Laubacher, Jacob. "Secondary Hochschild and Cyclic (Co)homologies." Doctoral dissertation, Bowling Green State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1489422065908758

    Chicago Manual of Style (17th edition)