Essays about: "Homological algebra"

Found 4 essays containing the words Homological algebra.

  1. 1. The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras

    University essay from Uppsala universitet/Algebra, logik och representationsteori

    Author : Mika Norlén Jäderberg; [2023]
    Keywords : Algebras; Finite-dimensional; Partially ordered sets; Modules; Quasi-hereditary; Ext-algebra; Schur algebra; Quiver; Path algebra; Categories; Morita equivalence; Yoneda product; Standard module; Homological algebra; Cohomology; Anick Chains;

    Abstract : Quasi-hereditary algebras are an important class of algebras with many appli-cations in representation theory, most notably the representation theory of semi-simple complex Lie-algebras. Such algebras sometimes admit an exact Borel sub-algebra, that is a subalgebra satisfying similar formal properties to the Borel sub-algebras from Lie theory. READ MORE

  3. 2. Relative Hochschild (co)homology

    University essay from Uppsala universitet/Algebra, logik och representationsteori

    Author : Jonathan Lindell; [2022]
    Keywords : Algebras; Hochschild cohomology; Relative Hochschild cohomology; Corings; Bocses; Homological algebra; Relative homological algebra; Spectral sequences; Relative homological algebra; Dual corings;

    Abstract : 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). READ MORE

  4. 3. Spectral sequences for composite functors

    University essay from KTH/Matematik (Avd.)

    Author : Adam Erlandsson; [2022]
    Keywords : Algebraic topology; homological algebra; spectral sequences; fibrations; derived functors; derived categories; Algebraisk topologi; homologisk algebra; spektralsekvenser; fibreringar; deriverade funktorer; deriverade kategorier;

    Abstract : Spectral sequences were developed during the mid-twentieth century as a way of computing (co)homology, and have wide uses in both algebraic topology and algebraic geometry.  Grothendieck introduced in his Tôhoku paper the Grothendieck spectral sequence, which given left exact functors $F$ and $G$ between abelian categories, uses the right-derived functors of $F$ and $G$ as initial data and converges to the right-derived functors of the composition $G\circ F. READ MORE

  5. 4. Homological Algebra for Quiver Representations

    University essay from Uppsala universitet/Algebra och geometri

    Author : Mateusz Stroiński; [2018]
    Keywords : ;

    Abstract : .... READ MORE