Computing the Hochschild Cohomology Groups of Some Families of Incidence Algebras

Gatica, María Andrea; Rey, Andrea

doi:10.1080/00927870600549543

Cited by 3 publications

(3 citation statements)

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“…Indeed, in terms of algebras given by quivers and relations, one-point extensions correspond to the process of adding a new vertex 'at the top' of the quiver -dually, one point coextensions correspond to adding a new vertex 'at the bottom' -and sufficiently simple quivers can be constructed inductively starting from a vertex by adding new vertices both on the top and on the bottom. See [8,9,10] for examples on how this inductive procedure for the computation of cohomology is carried out.…”

Section: 4mentioning

confidence: 99%

Applications of the change-of-rings spectral sequence to the computation of Hochschild cohomology

Suárez-Alvarez

2007

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We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information, we are able to completely describe the cohomology structure of monogenic algebras as well as some information on the structure of the cohomology in more general situations.We also show how to use the spectral sequence to reprove and generalize results of M. Auslander et al. about homological epimorphisms. We derive from this a rather general version of the long exact sequence due to D. Happel for a one-point (co)-extension of a finite dimensional algebra and show how it can be put to use in concrete examples.

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Section: 4mentioning

confidence: 99%

Applications of the change-of-rings spectral sequence to the computation of Hochschild cohomology

Suárez-Alvarez

2007

Preprint

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“…The incidence algebra of a finite poset is in fact a basic finite dimensional algebra and so it is also very natural to study them from the point of view of representation theory. A very incomplete list of papers on this subject is [2,9,[15][16][17][18]24,28,29,47,48].…”

Section: Introductionmentioning

confidence: 99%

“…17 If A = (Ai,..., A m ) is a partition of n, then we can define the following 1. A 1 = (Ai,..., Aj_i, Aj -1, Aj+i,..., A m ).…”

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confidence: 99%