Matrix representation of a cross product and related curl-based differential operators in all space dimensions

Abstract

A higher dimensional generalization of the cross product is associated with an adequate matrix multiplication. This index-free view allows for a better understanding of the underlying algebraic structures, among which are generalizations of Grassmann's, Jacobi's and Room's identities. Moreover, such a view provides a higher dimensional analogue of the decomposition of the vector Laplacian which itself gives an explicit index-free Helmholtz decomposition in arbitrary dimensions $n\ge 2$.

References in corpus (2)

• Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy
• $L^p$-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions

Cited by in corpus (2)

• Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions
• Korn-Maxwell-Sobolev inequalities for general incompatibilities