The Noncommutative Schemes of Generalized Weyl Algebras
نویسنده
چکیده
The first Weyl algebra over k, A1 = k〈x, y〉/(xy− yx− 1) admits a natural Z-grading by letting deg x = 1 and deg y = −1. Paul Smith showed that gr -A1 is equivalent to the category of quasicoherent sheaves on a certain quotient stack. Using autoequivalences of gr -A1, Smith constructed a commutative ring C, graded by finite subsets of the integers. He then showed gr -A1 ≡ gr -(C,Zfin). In this paper, we generalize results of Smith by using autoequivalences of a graded module category to construct rings with equivalent graded module categories. For certain generalized Weyl algebras, we use autoequivalences defined in a companion paper so that these constructions yield commutative rings.
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