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Showing 1 to 20 of 27 for “"Homological Algebra"”.
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Homological algebra
… directly relate with the functor Ext used in homological algebra."--Document.</p>
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Some Duality Results in Homological Algebra
… cohomology modules without recourse to linear algebra or symplectic geometry; these techniques can (when applicable) greatly improve computation time.
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Applications of Homological Algebra to Equational Theories
… equational theories such as groups or Boolean algebras can be defined by fewer equational axioms than the original axioms. However, it is not easy to determine if a given set of axioms is the smallest or not. Malbos and Mimram investigated a general method to find a lower bound of the …
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From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
… projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical action is closely related to the action of the type $B$ braid group on curves on the disc. Thus, our exposition can be seen as a type $B$ analogue of the work of Khovanov-Seidel. …
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From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
… projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical action is closely related to the action of the type $B$ braid group on curves on the disc. Thus, our exposition can be seen as a type $B$ analogue of the work of Khovanov-Seidel. …
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Razonamiento mecanizado en álgebra homológica
… version of a crucial algorithm in the field of Homological Algebra, known as "Perturbation Lemma". This lemma is intensively used in the software system "Kenzo", devoted to symbolic computation in Homological Algebra. To this end, we use the proof assistant "Isabelle". Our main motivations are …
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On Gorenstein Projective and Gorenstein Flat Modules
… metatheorem states, "Every result in classical homological algebra has a counterpart in Gorenstein homological algebra". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This …
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Gorenstein Injective Modules
One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite …
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Topics In Nonabelian Tensor Products Of Topological Groups
… product has been studied extensively in linear algebra with generalisations to abstract abelian group theory and modules. In this MSc thesis we study further generalisations of tensor products to non-abelian groups as well as topological groups. We encounter a rich existing theory of compact …
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On the local and global properties of information manifolds
… work, with the aim of understanding the global, algebrao-topological nature of information manifolds, we exhibit some of the necessary category theory required to effect a discussion of homological algebra in a general setting.
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The combinatorics of adinkras
… to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and accessible mathematical problems …
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The Ro (S¹)-graded equivariant homotopy of THH(Fp)
… odd dimensional [alpha]. These groups arise in algebraic K-theory computations, and are particularly important to the understanding of the algebraic K-theory of non-regular schemes. We also study RO(S¹)-graded TR-theory as an RO(S¹)-graded Mackey functor. Using Lewis and Mandell's homological …
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Cohomological dimension for C*-algebras
We define and explore invariants for C*-algebras that arise as cohomological dimensions for associated categories of operator space modules. The setting of exact categories provides us with a robust framework to utilise homological techniques.<br/><br/>We develop initial global dimension theorems …
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A Classifying Family of Spaces for the Cohomology of Profinite Groups
In the study of homological algebra, one useful tool for studying the cohomology of a discrete group is that group's classifying space. In some sense, the classifying space captures both the group itself and a description of its cohomology for any action of the group on any coefficient module. …
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Categorical semi-direct products in varieties of groups with multiple operators
… them in various classical varieties of such algebraic structures and apply the results to homological algebra and related areas of modern algebra. The context in which the study is done is a semiabelian category (that is, a pointed, Barr-exact and Bourn-protomodular category). The main result …
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Higher Scissors Congruence Groups of the Euclidean Plane
… groups are examples of computations in algebraic K-theory, which are known to be exceedingly difficult. In the Euclidean plane, I obtain a complete answer for the computation of an approximation of all higher scissors congruence groups, where that approximation is defined by permitting …
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Sequences of compact curvature
… geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and …
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On Bredon (co-)homological dimensions of groups
… way to attack this question is using methods in homological algebra. The natural choice for a cohomology theory to study G-CW-complexes with stabilisers in a given family F is known as Bredon cohomology. It is the study of cohomology in the category of OFG-modules. This category relates to models …
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Internal Yoneda Ext Groups, Central H-spaces, and Banded Types
… bands. The former are fundamental notions from homological algebra that support important computations in traditional homotopy theory. We develop these tools with the goal of supporting similar computations in our setting. In contrast, our results about central H-spaces and bands are new, even …
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