Homotopies for resolutions of skew-hook shapes

Buchsbaum, David A.; Taylor, Brian D.

doi:10.1016/s0196-8858(02)00523-7

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Letter Place Algebra1

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2004

2021

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Cited by 6 publications

(2 citation statements)

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“…For the reader who wants a more general definition of the letter-place set-up, we will borrow the brief summary given in [7]. We assume that we are given two free modules, L and P + , and we construct (see [11]) a bilinear pairing, of the divided power algebras D L and D P + into D L ⊗ P + .…”

Section: Letter Place Algebramentioning

confidence: 99%

Approaches to Resolution of Weyl Modules

Buchsbaum

Rota

2001

Advances in Applied Mathematics

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Section: Letter Place Algebramentioning

confidence: 99%

Approaches to Resolution of Weyl Modules

Buchsbaum

Rota

2001

Advances in Applied Mathematics

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“…The construction of homotopies is a basic tool in understanding the structure of these resolutions; and the best way of proving that these complexes are, in fact, resolutions. However, these homotopies have been constructed only in very special cases: the 2-rowed case (Buchsbaum and Rota, 1993), some steps for partitions (Buchsbaum and Rota, 2001, p. 176), hooks (Buchsbaum, 1998) and skew hooks (Buchsbaum and Taylor, 2003) (this last mentioned article contains a good exposition of the motivation of these studies).…”

Section: Introductionmentioning

confidence: 99%

Homotopies for the Generalized Bar Complex Associated to Certain 3-Rowed Weyl Modules

Sano¹

2006

Communications in Algebra

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In Buchsbaum and Rota (1994), the authors presented a generalized bar complex associated to certain 3-rowed Weyl modules and proved that this complex is in fact a resolution via an induction on the number of overlaps between the second and third rows and a fundamental exact sequence (Akin and Buchsbaum, 1985). In this article we study the structure of this resolution by constructing a splitting contracting homotopy for the complexes corresponding to certain shapes.

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