-adic Clifford algebras
Pairs of Clifford algebras of the Hurwitz type
For a given Hurwitz pair the existence of a bilinear mapping (where and ) denote the Clifford algebras of the quadratic forms and , respectively) generated by the Hurwitz multiplication “o” is proved and the counterpart of the Hurwitz condition on the Clifford algebra level is found. Moreover, a necessary and sufficient condition for "⭑" to be generated by the Hurwitz multiplication is shown.
Pfaffians, central simple algebras and similtudes.
Plane waves, biregular functions and hypercomplex Fourier analysis
Quadratic forms and Azumaya algebras.
Rectification : «Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique»
Relativistic wave equations with fractional derivatives and pseudodifferential operators.
Representations of the covering groups of the symmetric groups and their combinatorics.
Résultats récents sur la théorie des formes quadratiques
Revêtements «spinoriels» du groupe symplectique et indices de Maslov
Some partial differential equations in Clifford analysis
Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.
Some sharp inequalities for Dirac type operators.
Spinors in braided geometry
Let V be a ℂ-space, be a pre-braid operator and let This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra . If and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...
Structure fractals and para-quaternionic geometry
It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...
Support vector machine skin lesion classification in Clifford algebra subspaces
The present study develops the Clifford algebra within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis - ABCD. To generate the we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D vector onto...
Sur les algèbres de Clifford. II.
Sur les deux premiers invariants d'une forme quadratique
Sur les idéaux à gauche des algèbres de Clifford et les produits scalaires des spineurs
Sur les n-normes
Systèmes de puissances partiellement divisées