SPECIAL VINBERG CONES

Abstract The paper is devoted to the generalization of Vinberg theory homogeneous convex cones. Such a cone described as set “positive definite matrices” in commutative algebra ? n Hermitian T-matrices. These algebras are Euclidean Jordan and consist × matrices A = ( ij ), where ii ? ?, entry for i < j belongs some vector space V ; ????) $$ {a}_{ji}={a}_{ij}^{\ast }=\mathfrak{g}\left({a}_{ij},\cdot \right)\in {V}_{ij}^{\ast } a ji = ij ? g ? ? V dual }. . multiplication T-Hermitian defined by system “isometric” bilinear maps jk ? k , such that | ? ik |, lm . For 2, T-algebra 2 ) determined isomorphic called spin factor associated Lorentz timelike future directed vectors Minkowski ? 1,1 ? special rank 3 matrix S Clifford Cl( )-module together with an “admissible” metric ???? We generalize construction pseudo-Euclidean case, when 0 1 ? -graded admissible metric. ???? homogeneous, but not m 2; 3. calculate characteristic function Koszul-Vinberg this write down cubic polynomial. extend Baez’ quantum-mechanical interpretation ? case.