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A Note on the Green Invariants in Finite Group Modular Representative Theory

Authors:	Morton E Harris

Institution:	(1) Department of Mathematics, Statistics and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA

Abstract:	As in Finite Group Modular Representation Theory, let ${\mathcal{O}}$ be a commutative complete noetherian ring with an algebraically closed residue field k. Let G be a finite group and let N be a normal subgroup of G. First suppose that V is an indecomposable ${\mathcal{O}}(G/N)$ -module, so that Inf ^G _G/N(V) is an indecomposable ${\mathcal{O}}$ G-module. We relate the Green invariants of V as an ${\mathcal{O}}(G/N)$ -module to those of Inf ^G _G/N(V) as an ${\mathcal{O}}$ G-module. Secondly, let V and W be indecomposable ${\mathcal{O}}$ G-modules. Assume that W is an endo-permutation lattice and that $W \mathop\otimes\limits_{\mathcal{O}} V$ is also an indecomposable ${\mathcal{O}}$ G-module. We relate the Green invariants of the ${\mathcal{O}}$ G-modules V and $W \mathop\otimes\limits_{\mathcal{O}} V$ . (This situation arises under important Morita equivalences.) Received: December 11, 2006. Revised: August 22, 2007.

Keywords:	Primary 2020
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