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Multilinear forms and graded algebras
- Source :
-
Journal of Algebra . Nov2007, Vol. 317 Issue 1, p198-225. 28p. - Publication Year :
- 2007
-
Abstract
- Abstract: In this paper we investigate the class of the connected graded algebras which are finitely generated in degree 1, which are finitely presented with relations of degrees greater or equal to 2 and which are of finite global dimension D and Gorenstein. For D greater or equal to 4 we add the condition that these algebras are homogeneous and Koszul. It is shown that each such algebra is completely characterized by a multilinear form satisfying a twisted cyclicity condition and some other nondegeneracy conditions depending on the global dimension D. This multilinear form plays the role of a volume form and canonically identifies in the quadratic case to a nontrivial Hochschild cycle of maximal degree. Several examples including the Yang–Mills algebra and the extended 4-dimensional Sklyanin algebra are analyzed in this context. Actions of quantum groups are also investigated. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*ALGEBRA
*MATHEMATICAL analysis
*MULTILINEAR algebra
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 317
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 26678276
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2007.02.007