Regular algebras of dimension 4 and their \(A_\infty\)-Ext-algebras. (English) Zbl 1193.16014
Let \(k\) be an algebraically closed field. There are found 4 series of two-generated AS-regular \(\mathbb{Z}^2\)-graded associative \(k\)-algebras of global dimension 4 with two defining relations of degree 3 and 4. The generators have degrees \((1,0)\) and \((0,1)\). The defining relations depend on at most two parameters from \(k\). The list of algebras after deleting some special algebras in each series presents up to isomorphism all Noetherian generic in some sense AS regular two-generated algebras of global dimension 4.
These results are used for the problem of classification of quantum projective space of degree 3.
These results are used for the problem of classification of quantum projective space of degree 3.
Reviewer: Vyacheslav A. Artamonov (Moskva)
MSC:
| 16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16S15 | Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) |
| 16T20 | Ring-theoretic aspects of quantum groups |
| 14A22 | Noncommutative algebraic geometry |
| 16E10 | Homological dimension in associative algebras |
Keywords:
regular algebras; Noetherian Artin-Schelter regular connected graded algebras; global dimension; AS regular algebras; quantum projective spaceSoftware:
MapleReferences:
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