Abstract

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Let k be of a field of characteristic 0.  The first Weyl algebra A_1(k) = k<x,y>/(yx-xy-1) 

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is Z-graded with deg(x) = 1, deg(y) = -1, and is a simple ring of GK-dimension 2.  Sierra 

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has studied its category of graded modules and shown how to find all Z-graded algebras with 

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an equivalent graded module category.  Smith has also shown how the geometry of this example 

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is related to a certain stack.  Our goal is to study more general classes of Z-graded simple 

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rings to find more examples which may have interesting algebraic and geometric properties.  

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Specifically, we study the structure of Z-graded simple rings A with graded quotient ring Q 

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such that Q_0 is a field with trdeg Q_0 = GK A - 1.  As a special case, we can classify all 

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Z-graded simple rings of GK-dimension 2.  This is joint work with Jason Bell.