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Conference publications

Abstracts

XXII conference

Lorenc-invariant algebaic modulus

Koganov A.V.

NIISI RAN, Nakhimovsky st. 36, corp. 1, Moscow, 117218, Russia

1 pp. (accepted)

We build the algebraic hipercomplex numbers modulus wich havs the automorphism group isomorphic Lorenz group (Pention Algebra). Modulus dimension is 5. Coefficient feld is Real numbers. Generator set is 1,t,a,b,c. Generator Algebra: 1v=v1=v for v=1,t,a,b,c; tu=ut=0 for u=a,b,c; tt=1; aa=bb=cc= -1; ab=c, bc=a, ca=b, ba=-c, cb=-a, ac=-b. In Pention Algebra is true the weakened modularity: (xa+yb+zc)^{2}=x^2+y^2+z^2 (Euclidean norm in dimension 3); (st+xa+yb+zc)^{2}=s^2-x^2-y^2-z^2 (Minkovsky norm in dimension 4).

Outside of Quaternion subalgebra The Pention algebra is nonassociativity and it has zero divisor.

References.

I.L.Kantor, A.S.Solodovnikov. Hypercomplex numbers. Moscow, "Nauka", 1973.



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