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

Labbi, Mohammed Larbi

Arch. Math., Brno 49, No. 4, 241-271 (2013).

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.

Reviewer: Anton Galaev (Brno)

MSC:

53B20	Local Riemannian geometry
15A75	Exterior algebra, Grassmann algebras
15A24	Matrix equations and identities
15A63	Quadratic and bilinear forms, inner products

Keywords:

Cayley-Hamilton theorem; cofactor; characteristic coefficients; Laplace expansion; Newton identities; Jacobi’s formula; double form; Newton transformation; exterior product; Gauss-Bonnet theorem