McKay-type correspondence for AS-regular algebras. (Q2843983)
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scientific article; zbMATH DE number 6201843
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | McKay-type correspondence for AS-regular algebras. |
scientific article; zbMATH DE number 6201843 |
Statements
27 August 2013
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graded algebras
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quivers
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crossed products
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algebras of invariants
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McKay-type correspondence for AS-regular algebras. (English)
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Suppose that \(k\) is an algebraically closed field of characteristic zero and \(G\) a finite cyclic diagonal subgroup in \(\text{GL}(n,k)\). If \(A\) is an Artin-Schelter regular \(n\)-generated algebra then there is a natural action of \(G\) on \(A\). Let the global dimension of \(A\) be at least 2. Then under some additional assumptions the algebra of invariants \(A^G\) is derived equivalent to the preprojective algebra of the McKay quiver of \(G\).
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