Taylor towers of symmetric and exterior powers

Brenda Johnson; Randy McCarthy

Fundamenta Mathematicae, Tome 201 (2008), p. 197-216 / Harvested from The Polish Digital Mathematics Library

Résumé

We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, $D_{k} S p ⁿ$ and $D_{k} Λ ⁿ$ , in terms of the first terms in the Taylor towers of $S p^{t}$ and $Λ^{t}$ for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of $S p^{t}$ and $Λ^{t}$ . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for $D_{k} S p ⁿ$ and $D_{k} Λ ⁿ$ .

Publié le : 2008-01-01

Zbl 1182.55010

EUDML-ID : urn:eudml:doc:282858

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     author = {Brenda Johnson and Randy McCarthy},
     title = {Taylor towers of symmetric and exterior powers},
     journal = {Fundamenta Mathematicae},
     volume = {201},
     year = {2008},
     pages = {197-216},
     zbl = {1182.55010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-3-1}
}

Brenda Johnson; Randy McCarthy. Taylor towers of symmetric and exterior powers. Fundamenta Mathematicae, Tome 201 (2008) pp. 197-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-3-1/