Higher-dimensional orders, graph-orders, and derived equivalences

• Autores: K. W. Roggenkamp, M. Kauer
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 155, Nº 2, 2001, págs. 181-202
• Idioma: inglés
• DOI: 10.1016/s0022-4049(99)90107-x
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• Resumen

  • Green-orders (tree-orders) in the classical one-dimensional case are the setting, to understand p-adic blocks with cyclic defect of finite groups. Blocks with “cyclic defect” of Hecke orders however, are Green-orders over two-dimensional rings. Hecke orders of dihedral groups of order divisible by 4 are even defined over a three-dimensional ring. We extend the notion of Green-orders to orders associated to a locally embedded graph instead of a tree, and to general complete regular local noetherian ground rings of finite dimension. We extend the result, that classical tree-orders are derived equivalent to star-orders. We then use these results to clarify the derived equivalence classes of tame algebras of Dihedral type.