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arXiv · 1110.4336

Symmetry of Endomorphism Algebras

Adam A. Allan
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Abstract

Motivated by recent problems regarding the symmetry of Hecke algebras, we investigate the symmetry of the endomorphism algebra $E_P(M)$ for $P$ a $p$-group and $M$ a $kP$-module with $k$ a field of characteristic $p$. We provide a complete analysis for cyclic $p$-groups and the dihedral 2-groups. For the dihedral 2-groups, this requires the classification of the indecomposable modules in terms of string modules and band modules. We generalize our techniques to consider $E_Λ(M)$ for $Λ$ a Nakayama algebra, a local algebra, or even an arbitrary algebra.

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Adam A. Allan. 2011-12-09. Symmetry of Endomorphism Algebras. https://arxiv.org/abs/1110.4336

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