Hypercomplex algebras and geometry of spaces with fundamental form of an arbitrary order. (English) Zbl 1367.53014

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.


53A35 Non-Euclidean differential geometry
15A66 Clifford algebras, spinors
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[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. | | · 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).
[6] Efimov, N. V., Rozendorn, E. R.: Linear algebra and multidimensional geometry. Nauka, Moscow, 1975, (in Russian). · Zbl 1173.15301
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