Maximal graded orders over crystalline graded rings.

DOI10.1016/J.JALGEBRA.2010.04.028zbMATH Open1220.16012arXiv0903.4652OpenAlexW2052037140MaRDI QIDQ615819

Tim Neijens, Freddy M. J. van Oystaeyen

Publication date: 7 January 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Abstract: Crystalline graded rings are generalizations of certain classes of rings like generalized twisted group rings, generalized Weyl algebras, and generalized skew crossed products. When the base ring is a commutative Dedekind domain, two constructions are given for producing maximal graded orders. On the way, a new concept appears, so-called, spectrally twisted group. Some general properties of it are studied. At the end of the paper several examples are considered.

Full work available at URL: https://arxiv.org/abs/0903.4652

zbMATH Keywords

representationsglobal dimensionmaximal ordersDedekind domainscrystalline graded rings

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Graded rings and modules (associative rings and algebras) (16W50) Rings of differential operators (associative algebraic aspects) (16S32) Twisted and skew group rings, crossed products (16S35)

Cites Work

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• The Brauer splitting theorem and projective representations of finite groups over rings
• Krull dimension of generalized Weyl algebras and iterated skew polynomial rings: Commutative coefficients
• Generalized 2-cocycles of finite groups and maximal orders
• Simple holonomic modules over the second Weyl algebra \(A_2\)
• Introducing crystalline graded algebras.
• Generalized twisted group rings.

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