Geometric Structures over Hypercomplex Algebras
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 145 (2018), pp. 123-137.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider various algebras of hypercomplex numbers and geometric structures over them and discuss certain applications of these structures in theoretical physics.
Keywords: hypercomplex number, fundamental form.
Mots-clés : quaternion
@article{INTO_2018_145_a5,
     author = {I. M. Burlakov and M. P. Burlakov},
     title = {Geometric {Structures} over {Hypercomplex} {Algebras}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {123--137},
     publisher = {mathdoc},
     volume = {145},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_145_a5/}
}
TY  - JOUR
AU  - I. M. Burlakov
AU  - M. P. Burlakov
TI  - Geometric Structures over Hypercomplex Algebras
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 123
EP  - 137
VL  - 145
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_145_a5/
LA  - ru
ID  - INTO_2018_145_a5
ER  - 
%0 Journal Article
%A I. M. Burlakov
%A M. P. Burlakov
%T Geometric Structures over Hypercomplex Algebras
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 123-137
%V 145
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_145_a5/
%G ru
%F INTO_2018_145_a5
I. M. Burlakov; M. P. Burlakov. Geometric Structures over Hypercomplex Algebras. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 145 (2018), pp. 123-137. http://geodesic.mathdoc.fr/item/INTO_2018_145_a5/

[1] Burlakov I. M., Burlakov M. P., Vvedenie v giperkompleksnyi analiz, LAMBERT Academic Publishing, 2017

[2] Burlakov I. M., Burlakov M. P., Geometricheskie struktury lineinykh algebr, LAMBERT Academic Publishing, 2017

[3] Burlakov M. P., “Kliffordovy rassloeniya i kalibrovochnye polya”, Gravitatsiya i teoriya otnositelnosti, v. 23, KGU, Kazan, 1986, 30–36

[4] Burlakov M. P., “Kliffordovy svyaznosti na rimanovykh prostranstvakh”, Izv. vuzov. Mat., 1990, no. 7, 3–7

[5] Burlakov M. P., “Kliffordovy struktury na mnogoobraziyakh”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 30, VINITI, M., 2002, 220–257

[6] Burlakov M. P., Pokazeev V. V., Freidenzon L. E., “Kliffordov analiz. I. $\Delta$-algebry Klifforda”, Dep. v VINITI, 1988, no. 1959-V88

[7] Burlakov M. P., Pokazeev V. V., Freidenzon L. E., “Kliffordov analiz. II. Integralnye predstavleniya”, Dep. v VINITI, 1988, no. 1960-V88

[8] Burlakov M. P., Pokazeev V. V., Freidenzon L. E., “Kliffordov analiz. III. Ryady Teilora”, Dep. v VINITI, 1988, no. 1961-V88

[9] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, KGU, Kazan, 1985 | MR

[10] Garasko G. I., Nachala finslerovoi geometrii dlya fizikov, TETRU, M., 2009

[11] Dirak P. A. M., K sozdaniyu kvantovoi teorii polya, Nauka, M., 1990

[12] Kartan E., Teoriya spinorov, GIIL, M., 1947

[13] Kotelnikov A. P., Vintovoe schislenie i nekotorye prilozheniya ego k geometrii i mekhanike, Kazan, 1895

[14] Proskuryakov I. V., Sbornik zadach po lineinoi algebre, Nauka, M., 1967

[15] Rozenfeld B. A., Neevklidovy geometrii, Gostekhizdat, M., 1954 | MR

[16] Rund Kh., Differentsialnaya geometriya finslerovykh prostranstv, Nauka, M., 1981

[17] Bambusi D., “Clifford algebra description of non-Abelian gauge fields”, J. Geom. Phys., 7:1 (1990), 1–12 | DOI | MR | Zbl

[18] Barker G. P., Urani J. R., “Dirac general covariance and tetrads, I. Clifford and Lie bundles and torsion”, J. Math. Phys., 10 (1983), 2407–2410 | MR

[19] Blau M., “Connections on Clifford bundles and the Dirac operator”, Lett. Math. Phys., 13:1 (1987), 83–92 | DOI | MR | Zbl

[20] Brauer R., Weyl H., “Spinors in $n$ dimensions”, Am. J. Math., 57 (1935), 425–449 | DOI | MR

[21] Clifford W. K., “Applications of Grassmann's extensive algebra”, Am. J. Math., 1 (1878), 350–358 | DOI | MR | Zbl

[22] Delanghe R., Brackx F., Sommen F., Clifford analysis, Pitnam Publ., Boston–London–Melbourne, 1982 | MR | Zbl

[23] Dimakis A., Muller-Hoissen F., “Clifford calculus with applications to classical field theories”, Class. Quantum Grav., 8:11 (1991), 2093–2132 | DOI | MR | Zbl

[24] Dixon G., “Fermionic Clifford algebras and supersymmetry”, Clifford Algebras and Their Applications in Mathematical Physics, Proc. NATO and SERC Workshop (Canterbury, 15-27 Sept. 1985), Dordrecht, 1986, 393–398 | DOI | MR

[25] Grassmann H. G., Gesammelte mathematische und physikalische Werke, Berlin, 1894–1911 | MR | Zbl

[26] Hamilton W. R., Lectures on Quaternions, Dublin, 1853

[27] Maia A. (Jr.), Recami E., Valbur R. (Jr.), Rosa Marcio A. F., “Magnetic monopoles without string in the Kaller–Clifford algebra bundle: a geometrical interpretation”, J. Math. Phys., 31:2 (1990), 502–505 | DOI | MR | Zbl

[28] Marcinek W., “Clifford structures on real vector spaces and manifolds”, Repts. Math. Phys., 27:3 (1989), 361–375 | DOI | MR | Zbl