×

On some algebraic identities and the exterior product of double forms. (English) Zbl 1299.53043

The paper deals with double forms, i.e., elements of the tensor product of two copies of the exterior algebra over a vector space. Different operation over double forms are described. Some classical identities and theorems are reformulated in terms of double forms, e.g., Jacobi formula for the determinant, Cayley-Hamilton theorem. Relation with an infinitesimal version with the Gauss-Bonet theorem is discussed. Finally, several open questions are proposed.

MSC:

53B20 Local Riemannian geometry
15A75 Exterior algebra, Grassmann algebras
15A24 Matrix equations and identities
15A63 Quadratic and bilinear forms, inner products
PDFBibTeX XMLCite
Full Text: DOI arXiv