Geometry of linear algebras. (English. Russian original) Zbl 1532.15016
J. Math. Sci., New York 277, No. 5, 711-717 (2023); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 182, 3-9 (2020).
Summary: In this paper, we consider spaces whose geometry is generated by a homogeneous function of degree \(m \geq 2\), which is invariant under the action of some subgroup of the linear group of the given space. A general method is proposed and examples of realization of such spaces on linear algebras are given.
MSC:
| 15A66 | Clifford algebras, spinors |
| 15A30 | Algebraic systems of matrices |
| 51M15 | Geometric constructions in real or complex geometry |
References:
| [1] | I. M. Burlakov and M. P. Burlakov, Geometric Structures of Linear Algebras [in Russian], LAP LAMBERT (2016). · Zbl 1367.53011 |
| [2] | M. P. Burlakov, Hamiltonian Algebras [in Russian], Graf Press, Moscow (2006). |
| [3] | M. P. Burlakov, Algebraic Methods in Mathematical Physics [in Russian], Groznyi (1985). |
| [4] | G. I. Garas’ko, Foundations of Finsler Geometry for Physicists [in Russian], TETRU, Moscow (2009). |
| [5] | Klein, F., Elementary Mathematics from an Advanced Standpoint (2004), Mineola, New York: Dover, Mineola, New York · JFM 58.1007.02 |
| [6] | A. S. Mishchenko, Vector Bundles and Their Applications [in Russian], Nauka, Moscow (1984). · Zbl 0569.55001 |
| [7] | B. A. Rozenfeld, Non-Euclidean Geometries [in Russian], GITTL, Moscow (1955). |
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