Essays about: "cohomology"
Showing result 1 - 5 of 13 essays containing the word cohomology.
-
1. An Introduction to Symmetry Protected Topological Phases
University essay from Uppsala universitet/Teoretisk fysikAbstract : In this thesis, we aim to display characteristics of symmetry protected topological phases within quantum mechanics (QM). Building on well known aspects of QM, we relate the formalism to basic group representation theory, and review the connection between projective symmetries and protected vacuum degeneracies. READ MORE
-
2. The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras
University essay from Uppsala universitet/Algebra, logik och representationsteoriAbstract : 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. Relative Hochschild (co)homology
University essay from Uppsala universitet/Algebra, logik och representationsteoriAbstract : 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. Spectral sequences for composite functors
University essay from KTH/Matematik (Avd.)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. De Rham Cohomology From Infinitesimal Handles
University essay from Uppsala universitet/Geometri och fysikAbstract : Compact smooth n-dimensional manifolds admit handle decompositions. Here a k-handleis a product of disks of dimension k and (n-k) and the decomposition says how the handles areglued together. If the manifold is connected it has a handle decomposition with only one0-handle. READ MORE
