Diagonalizability of elements of a group algebra

Let G be a group and K a fields of characteristic 0. Let f be an element of the group algebra K[G]. Let X(f) be the matrix of the left-multiplication action of f on K[G]. We determine the eigenvalues and their multiplicities of X(f) when f is a central element of G, when f is an element of the desce...

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Bibliographic Details
Main Author: Randriamaro, Hery
Contributors: Welker, Volkmar (Prof. Dr.) (Thesis advisor)
Format: Dissertation
Language:German
Published: Philipps-Universität Marburg 2012
Mathematik und Informatik
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Online Access:PDF Full Text
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Summary:Let G be a group and K a fields of characteristic 0. Let f be an element of the group algebra K[G]. Let X(f) be the matrix of the left-multiplication action of f on K[G]. We determine the eigenvalues and their multiplicities of X(f) when f is a central element of G, when f is an element of the descent algebra of K[G] for a coxeter group G, and when f is a special element of K[G] for a symmetric group G.
DOI:https://doi.org/10.17192/z2012.0468