We survey the results concerning the graded identities of the infinite dimensional Grassmann algebra. 2010 MSC: 16R10, 16P90, 16S10, 16W50

Alfred North Whitehead promoted the idea of UNIVERSAL ALGEBRA in his monumental treatise of 1897 [1]. He proposed two candidates for this lofty title, the algebra of Boole and Grassmann’s Algebra of Extension. Boolean algebra has since secured universality status in Set Theory and Symbolic Logic, although only the former is universally known and used by mathematicians. However, Whitehead’s work...

In this paper an analytic formulation of the statics and the instantaneous kinematics of robot manipulators based on the Grassmann-Cayley algebra is presented. The notions of twist, wrench, twist space and wrench space are mathematically represented by the concept of extensors of this algebra and the reciprocity relation between twist and wrench spaces of partially constrained rigid bodies is r...

Grassmann’s epistemological insights have attracted less attention than his mathematical results. Mathematicians have considered him as a precursor of modern mathematical theories – vector algebra, exterior algebra, Clifford algebra, and geometric algebra –, paying attention to the development of mathematical results rather than to the philosophical differences between Grassmann’s own project a...

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of thes...