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1	Relative Hochschild (co)homology Lindell, Jonathan January 2022 (has links) 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. Algebra and Logic Algebra och logik
2	Bounding The Hochschild Cohomological Dimension Kratsios, Anastasis 08 1900 (has links) Ce mémoire a deux objectifs principaux. Premièrement de développer et interpréter les groupes de cohomologie de Hochschild de basse dimension et deuxièmement de borner la dimension cohomologique des k-algèbres par dessous; montrant que presque aucune k-algèbre commutative est quasi-libre. / The aim of this master’s thesis is two-fold. Firstly to develop and interpret the low dimensional Hochschild cohomology of a k-algebra and secondly to establish a lower bound for the Hochschild cohomological dimension of a k-algebra; showing that nearly no commutative k-algebra is quasi-free. Relative Homological Algebra Dimension Theory Noncommutative Geometry Hochschild Cohomology Noncommutative Algebra Algebraic Geometry Homological Algebra Algèbre homologique Géométrie Algébrique Noncommutative Differential Forms
3	A classification of localizing subcategories by relative homological algebra Nadareishvili, George 16 October 2015 (has links) No description available. 510 C-algebra Kasparov category homological algebra triangulated category non-commutative topology filtrations of C-algebras C*-algebras over a topological space localizing subcategory localising subcategory Bivariant K-theory Filtrated K-theory relative homological algebra bootstrap class KK-theory ring of upper triangular matrices Mathematics (PPN61756535X)

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