We attach the degenerate signature (n,0,1) to the dual Grassmann algebra of projective space to obtain a real Clifford algebra which provides a powerful, efficient model for euclidean geometry. We avoid problems with the degenerate metric by constructing an algebra isomorphism between the Grassmann algebra and its dual that yields non-metric meet and join operators. We focus on the cases of n=2...

Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane R = k〈x, y〉/(xy − yx− y). Complete description of irreducible components of the representation variety mod(R,n) obtained for any dimension n, it is shown that the variety is equidimensional. The influence of the property of the non-commutati...

We consider non-degenerate graph immersions into affine space An+1 whose cubic form is parallel with respect to the Levi-Civita connection of metric. There exists a correspondence between such and pairs (J,?), where J an n-dimensional real Jordan algebra ? trace on J. Every immersion can be extended complete symmetric covering maximal connected component zero in set quasi-regular elements It im...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.

In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.

Let E/k be a cubic field extension and J a simple exceptional Jordan algebra of degree 3 over k. Then £ is a reducing field of J if and only if E is isomorphic to a (maximal) subfield of some isotope of /. If k has characteristic not 2 or 3 and contains the third roots of unity then every simple exceptional Jordan division algebra of degree 3 over k contains a cyclic cubic subfield. Exceptional...

In this paper, we investigate the issue of error bounds for symmetric cone complementarity problems (SCCPs). In particular, we show that the distance between an arbitrary point in Euclidean Jordan algebra and the solution set of the symmetric cone complementarity problem can be bounded above by some merit functions such as FischerBurmeister merit function, the natural residual function and the ...

A Clifford algebra has three major multiplications: inner product, outer product and geometric product. Accordingly, the same Clifford algebra has three versions: Clifford vector algebra, which features on inner products and outer products of multivectors; Clifford bracket algebra, which features on pseudoscalars and inner products of vectors; Clifford geometric algebra, which features on geome...