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Keywords:
Hypercomplex algebras; geometry of spaces with fundamental form; Clifford algebras
Hypercomplex algebras; geometry of spaces with fundamental form; Clifford algebras
Summary:
The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.
References:
[1] Rosenfeld, B. A.: Neevklidovy geometrii. GITTL, Moscow, 1955, (in Russian).
[2] Burlakov, M. P.: Clifford structures on manifolds. J. Math. Sci. 89, 3 (1998), 1311–1333, Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 30, Geometriya-3, 1995. DOI 10.1007/BF02414874 | MR 1619716 | Zbl 0930.53030
[3] Burlakov, M. P.: Gamiltonovy algebry. Graf-press, Moscow, 2006, (in Russian).
[4] Chelzen, F., Martin, A.: Kvarki i leptony. Mir, Moscow, 1987, (in Russian).
[5] Penrouz, R., Rindler, V.: Spinory i prostranstvo-vremja. Mir, Moscow, 1987, (in Russian). MR 0908073
[6] Efimov, N. V., Rozendorn, E. R.: Linear algebra and multidimensional geometry. Nauka, Moscow, 1975, (in Russian).
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