Maximal Graded Orders over Crystalline Graded Rings
Tim Neijens, Fred Van Oystaeyen
TL;DR
This paper introduces methods to construct maximal graded orders over crystalline graded rings, a generalization of various algebraic structures, and explores a new concept called spectrally twisted groups with several examples.
Contribution
It presents two new constructions for maximal graded orders over crystalline graded rings and introduces the novel concept of spectrally twisted groups.
Findings
Two constructions for maximal graded orders are provided.
Spectrally twisted groups are defined and studied.
Several examples illustrate the concepts.
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras