Graded algebras and multilinear forms. (English) Zbl 1105.16020
Summary: We give a description of the connected graded algebras which are finitely generated and presented of global dimension 2 or 3 and which are Gorenstein. These algebras are constructed from multilinear forms. We generalize the construction by associating homogeneous algebras to multilinear forms. The homogeneous algebras which are Koszul-Gorenstein of finite global dimension are of this type.
MSC:
| 16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16S37 | Quadratic and Koszul algebras |
| 16S15 | Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) |
Keywords:
connected graded algebras; finitely generated algebras; finitely presented algebras; multilinear forms; homogeneous algebras; Koszul-Gorenstein algebrasReferences:
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