Tate Cohomology of Finite Dimensional Hopf Algebras
| dc.contributor | Witherspoon, Sarah | |
| dc.creator | Nguyen, Van Cat | |
| dc.date.accessioned | 2016-08-01T05:30:13Z | |
| dc.date.accessioned | 2017-04-07T20:10:47Z | |
| dc.date.available | 2016-08-01T05:30:13Z | |
| dc.date.available | 2017-04-07T20:10:47Z | |
| dc.date.created | 2014-08 | |
| dc.date.issued | 2014-06-19 | |
| dc.description.abstract | Let A be a finite dimensional Hopf algebra over a field k. In this dissertation, we study the Tate cohomology ?* (A, k) and Tate-Hochschild cohomology (HH) ?* (A, A) of A, and their properties. We introduce cup products that make them become graded-commutative rings and establish the relationship between these rings. In particular, we show ?* (A, k) is an algebra direct summand of (HH) ?* (A, A) as a module over ?* (A, k). When A is a finite group algebra RG over a commutative ring R, we show that the Tate-Hochschild cohomology ring (HH) ?* (RG, RG) of RG is isomorphic to a direct sum of the Tate cohomology rings of the centralizers of conjugacy class representatives of G. Moreover, our main result provides an explicit formula for the cup product in (HH) ?* (RG, RG) with respect to this decomposition. When A is symmetric, we show that there are finitely generated A-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring ?* (A, k) of A. It turns out that if a module in a connected component of the stable Auslander-Reiten quiver associated to A has finitely generated Tate cohomology, then so does every module in that component. | |
| dc.identifier.uri | http://hdl.handle.net/1969.1/153306 | |
| dc.language.iso | en | |
| dc.subject | Tate cohomology | |
| dc.subject | stable cohomology | |
| dc.subject | Hopf algebras | |
| dc.title | Tate Cohomology of Finite Dimensional Hopf Algebras | |
| dc.type | Thesis |