Some recent results on Hochschild homology of commutative algebras.
This article is a brief survey of the recent results obtained by several authors on Hochschild homology of commutative algebras arising from the second author’s paper [21].
Some Remarks on Module Rigidity Over Local Rings.
Some results on central extensions of crossed modules.
Some results on -flat dimension of modules
In this paper, we study some properties of -flat -modules, where is a semidualizing module over a commutative ring and we investigate the relation between the -yoke with the -yoke of a module as well as the relation between the -flat resolution and the flat resolution of a module over -closed rings. We also obtain a criterion for computing the -flat dimension of modules.
Some results on homotopy theory of modules
Seguendo le idee presentate nei lavori [1] e [2] si studiano le proprietà dei gruppi di -omotopia per moduli ed omomorfismi di moduli.
Sous-groupes fonctoriels et relativisations
Sous-quotients et relations induites dans les catégories exactes
Spaces associated to quadratic endofunctors of the category of groups.
Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π2(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.
Spectral sequences and relative cohomology
Split extensions and semidirect products of unitary magmas
We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras
We revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in separate, joint work of the author on the simplicial and cyclic cohomology of band semigroup algebras). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [2] and [5].
Stability of algebraic inverse systems, I: Stability, weak stability and the weakly-stable socle
Stable and costable preradicals
Stable derived functors of the second symmetric power functor, second exterior power functor and Whitehead gamma functor
Stable derived functors, the Steenrod algebra and homological algebra in the category of functors
We present a very short way of calculating additively the stable (co)homology of Eilenberg-MacLane spaces K(ℤ/p,n). Our method depends only on homological algebra in appropriate categories of functors.
Stable short exact sequences and the maximal exact structure of an additive category
It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
Stacks and the homotopy theory of simplicial sheaves.
State-sum invariants of knotted curves and surfaces from quandle cohomology.
Steenrod Squares in Cotor
(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras
Let be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective -modules under the condition that is a cocompatible -bimodule, we establish a recollement of the stable category . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over .