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OPERADS AND JET MODULES.
- Source :
-
International Journal of Geometric Methods in Modern Physics . Dec2005, Vol. 2 Issue 6, p1133-1186. 54p. - Publication Year :
- 2005
-
Abstract
- Let A be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of A-modules. We define certain symmetric product functors of such modules generalizing the tensor product of modules over commutative algebras, which we use to define the notion of a jet module. This in turn generalizes the notion of a jet module over a module over a classical commutative algebra. We are able to define Atiyah classes (i.e., obstructions to the existence of connections) in this generalized context. We use certain model structures on the category of A-modules to study the properties of these Atiyah classes. The purpose of the paper is not to present any really deep theorem. It is more about the right concepts when dealing with modules over an algebra that is defined over an arbitrary operad, i.e., the aim is to show how to generalize various classical constructions, including modules of jets, the Atiyah class and the curvature, to the operadic context. For convenience of the reader and for the purpose of defining the notations, the basic definitions of the theory of operads and model categories are included. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MODULES (Algebra)
*COMMUTATIVE algebra
*MATHEMATICAL models
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 02198878
- Volume :
- 2
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- International Journal of Geometric Methods in Modern Physics
- Publication Type :
- Academic Journal
- Accession number :
- 19153409
- Full Text :
- https://doi.org/10.1142/S0219887805000995