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Z-GRADED SIMPLE RINGS.
- Source :
-
Transactions of the American Mathematical Society . Jun2016, Vol. 368 Issue 6, p4461-4496. 36p. - Publication Year :
- 2016
-
Abstract
- The Weyl algebra over a field k of characteristic 0 is a simple ring of Gelfand-Kirillov dimension 2, which has a grading by the group of integers. We classify all Z-graded simple rings of GK-dimension 2 and show that they are graded Morita equivalent to generalized Weyl algebras as defined by Bavula. More generally, we study Z-graded simple rings A of any dimension which have a graded quotient ring of the form K[t, t-1; σ] for a field K. Under some further hypotheses, we classify all such A in terms of a new construction of simple rings which we introduce in this paper. In the important special case that GKdimA = tr. deg(K/k) + 1, we show that K and σ must be of a very special form. The new simple rings we define should warrant further study from the perspective of noncommutative geometry. [ABSTRACT FROM AUTHOR]
- Subjects :
- *WEYL groups
*WEYL space
*GEOMETRY
*INTEGERS
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 368
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 112685969
- Full Text :
- https://doi.org/10.1090/tran/6472