The variety of an indecomposable module is connected (Q795928)

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scientific article; zbMATH DE number 3863471
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English
The variety of an indecomposable module is connected
scientific article; zbMATH DE number 3863471

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    The variety of an indecomposable module is connected (English)
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    1984
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    Let G be a finite group and K an algebraically closed field of characteristic \(p>0\). To any finitely generated KG-module M a homogeneous affine variety V(M) is associated via cohomology. In [J. Algebra 85, 104- 143 (1983; Zbl 0526.20040), Thm. 8.2] the author had shown that if G is an elementary abelian group of order \(p^ n\) and M an indecomposable periodic KG-module then V(M) is a line in \(K^ n\). Here he obtains the best generalization of this result and shows that if \=V(M) is the corresponding projective variety, then Theorem: If M is an indecomposable KG-module then \=V(M) is connected.
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    connectedness of variety of indecomposable module
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    homogeneous affine variety
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    cohomology
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    indecomposable periodic KG-module
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    projective variety
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