We study relative homological algebra and relative Hochschild cohomology. We dualise the construction in [Cib+21b] for a ring extension B ⊆ A to construct a long nearly exact sequence for the relative Hochschild cohomology HH∗(A|B), the Hochschild cohomology HH∗(A) and the Hochschild cohomology HH∗(B,A). Parallel to this we also study corings and the associated Cartier cohomology and Hochschild cohomology. Given an A-coring C and its right algebra R we have induced maps ExtiA(M, N) → ExtiR(R⊗A M, R⊗A N) by the induction functor. We characterise the vanishing of the Hochschild cohomology of the coring in terms of these induced maps being isomorphisms for degrees greater than or equal to one.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-515067 |
| Date | January 2022 |
| Creators | Lindell, Jonathan |
| Publisher | Uppsala universitet, Algebra, logik och representationsteori |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. project report ; 2023:39 |
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