EXTENSION OF SINE–GORDON FIELD THEORY FROM GENERALIZED CLIFFORD ALGEBRAS

Hyperbolic Polynomials and Generalized Clifford Algebras

We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford algebras for a new approach to the problem. Our main result is that if −1 is not a sum of hermitian squares in the Clifford algebra of a hyperbolic polynomial, t...

Polyvector Super-poincare Algebras, M,f Theory Algebras and Generalized Supersymmetry in Clifford-spaces

Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic Supersymmetric pointparticle action in Clifford-space backgrounds. The relativistic Supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the ...

On Clifford Theory of Vertex Operator Algebras

Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r, p, n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hec...

Generalized Clifford Algebras and the Last Fermat Theorem

Abstract One shows that the Last Fermat Theorem is equivalent to the statement that all rational solutions x + y = 1 of equation (k ≥ 2) are provided by an orbit of rationally parametrized subgroup of a group preserving k–ubic form. This very group naturally arrises in the generalized Clifford algebras setting [1]. I. The stroboscopic motion of the independent oscilatory degree of freedom is gi...