Burlakov, Mikhail P.; Burlakov, Igor M.; Jukl, Marek Hypercomplex algebras and geometry of spaces with fundamental form of an arbitrary order. (English) Zbl 1367.53014 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 55, No. 1, 31-38 (2016). 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. Cited in 1 Document MSC: 53A35 Non-Euclidean differential geometry 15A66 Clifford algebras, spinors Keywords:hypercomplex algebras; fundamental form of arbitrary order; Clifford algebras PDF BibTeX XML Cite \textit{M. P. Burlakov} et al., Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 55, No. 1, 31--38 (2016; Zbl 1367.53014) Full Text: Link OpenURL 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. | | · 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.