Graded commutative algebras: examples, classification, open problems

We consider \G-graded commutative algebras, where \G is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on the subject. We then give a recent classification result and formulate an open problem

Unified Octonionic Representation of the 10-13 Dimensional Clifford Algebra

We give a one dimensional octonionic representation of the different Clifford algebra Cliff(5,5)\sim Cliff(9,1), Cliff(6,6)\sim Cliff(10,2) and lastly Cliff(7,6)\sim Cliff(10,3) which can be given by (8x8) real matrices taking into account some suitable manipulation rules.Comment: RevTex file, 19 pages, to be published in Int. J. of Mod. Phys.

Disproof of Bell's Theorem: Further Consolidations

The failure of Bell's theorem for Clifford algebra valued local variables is further consolidated by proving that the conditions of remote parameter independence and remote outcome independence are duly respected within the recently constructed exact, local realistic model for the EPR-Bohm correlations. Since the conjunction of these two conditions is equivalent to the locality condition of Bell, this provides an independent geometric proof of the local causality of the model, at the level of microstates. In addition to local causality, the model respects at least seven other conceptual and operational requirements, arising either from the predictions of quantum mechanics or the premises of Bell's theorem, including the Malus's law for sequential spin measurements. Since the agreement between the predictions of the model and those of quantum mechanics is quantitatively precise in all respects, the ensemble interpretation of the entangled singlet state becomes amenable.Comment: 11 pages; This is a followup to arXiv:quant-ph/0703179; see also arXiv:quant-ph/070324