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Article

Burlakov, Igor M. ; Jukl, Marek
Geometry of Cyclic and Anticylic Algebras. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 55 (2016), issue 2, pp. 23-27
MSC: 15A66, 53B30, 57R15 | Zbl 1367.53013
Keywords:
Cyclic and anticyclic algebras; composition algebras; determinants of elements of linear algebras; multiplicative functions; groups of motions
Summary:
The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function.
References:
[1] Vishnevsky, V. V., Shirokov, A. P., Shurigin, V. V.: Spaces over Algebras. Kazan University, Kazan, 1985, (in Russian).
[2] Shestakov, I. P., Shirokov, A. I., Slin’ko, A. M., Zhevlakov, K. A.: Rings that are nearly associative. Academic Press, New York, 1982. MR 0668355
[3] Burlakov, M. P.: Gamiltonovy algebry. Graf-press, Moscow, 2006, (in Russian).
[4] Burlakov, M. P., Burlakov, I. M., Jukl, M.: Hypercomplex algebras and geometry of spaces with fundamental form of an arbitary order. Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 55, 1 (2016), 31–38. MR 3674597
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