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For which pseudo reflection groups are the p-adic polynomial invariants again a polynomial algebra?
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For which pseudo reflection groups are the p-adic polynomial invariants again a polynomial algebra?
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Topological realization of a family of pseudoreflection groups
No full textWe are interested in a topological realization of a family of pseudoreflection groups G ⊂ GL(n,{\sym F}_p ); i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants {\sym F}_p [x_1,..., x_n]^G. Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over {\sym F}_p can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product where q divides p - 1 and where p is odd. Let G be such a subgroup acting on the polynomial algebra A:= {\sym F}_p [x_1,..., x_n]. We show that there exists a space X such that H*(X;{\sym F}_p )≅ A^G which is again a polynomial algebra. Examples of polynomial algebras of this form are given by the mod-p cohomology of the classifying spaces of special orthogonal groups or of symplectic groups.
The construction uses products of classifying spaces of unitary groups as building blocks which are glued together via information encoded in a full subcategory of the orbit category of the group G. Using this construction we also show that the homotopy type of the p-adic completion of these spaces is completely determined by the mod-p cohomology considered as an algebra over the Steenrod algebra. Moreover, we calculate the set of homotopy classes of self maps of the completed spaces
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