On Indecomposable and Imprimitive Modules for Finite Groups – A  G ‐Algebra Approach | Zendy

Fottner Hubert | Zendy; Külshammer Burkhard | Zendy

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On Indecomposable and Imprimitive Modules for Finite Groups – A G ‐Algebra Approach

Author(s) -

Fottner Hubert,

Külshammer Burkhard

Publication year - 1999

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610799007541

Subject(s) - indecomposable module , discrete valuation ring , mathematics , residue field , algebraically closed field , discrete valuation , pure mathematics , algebra over a field , simple module , finitely generated abelian group , rank (graph theory) , discrete mathematics , combinatorics , simple (philosophy) , field (mathematics) , philosophy , epistemology

One of the most useful results in modular representation theory of finite groups is Green's indecomposability theorem [ 4 ]. In order to state it in a simple form, let us fix a complete discrete valuation ring O of characteristic 0 with algebraically closed residue field F of characteristic p ≠0. Unless stated otherwise, all our modules will be free of finite rank over O or F, respectively. In its most popular form, Green's theorem says the following.

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