Algebraic Connections and Curvature in Fibrations Bundles of Associative Algebras

Igor M. Burlakov

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 2, page 17-21
  • ISSN: 0231-9721

Abstract

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In this article fibrations of associative algebras on smooth manifolds are investigated. Sections of these fibrations are spinor, co spinor and vector fields with respect to a gauge group. Invariant differentiations are constructed and curvature and torsion of invariant differentiations are calculated.

How to cite

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Burlakov, Igor M.. "Algebraic Connections and Curvature in Fibrations Bundles of Associative Algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.2 (2016): 17-21. <http://eudml.org/doc/287909>.

@article{Burlakov2016,
abstract = {In this article fibrations of associative algebras on smooth manifolds are investigated. Sections of these fibrations are spinor, co spinor and vector fields with respect to a gauge group. Invariant differentiations are constructed and curvature and torsion of invariant differentiations are calculated.},
author = {Burlakov, Igor M.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Algebraic fibration; spinor; co spinor; vector field; field of connection; invariant differentiation; curvature; torsion},
language = {eng},
number = {2},
pages = {17-21},
publisher = {Palacký University Olomouc},
title = {Algebraic Connections and Curvature in Fibrations Bundles of Associative Algebras},
url = {http://eudml.org/doc/287909},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Burlakov, Igor M.
TI - Algebraic Connections and Curvature in Fibrations Bundles of Associative Algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 2
SP - 17
EP - 21
AB - In this article fibrations of associative algebras on smooth manifolds are investigated. Sections of these fibrations are spinor, co spinor and vector fields with respect to a gauge group. Invariant differentiations are constructed and curvature and torsion of invariant differentiations are calculated.
LA - eng
KW - Algebraic fibration; spinor; co spinor; vector field; field of connection; invariant differentiation; curvature; torsion
UR - http://eudml.org/doc/287909
ER -

References

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  1. Dubrovin, B. A., Novikov, S. P., Fomenko, A. T., 10.1090/S0273-0979-1985-15366-2, . Bull. Amer. Math. Soc. (N.S.) 13, 1 (1985), 62–65, (Nauka, Moscow, 1978, in Russian). (1985) MR0566582DOI10.1090/S0273-0979-1985-15366-2
  2. Burlakov, I. M., Geometric Structures in Bundles of Associative Algebras, . Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 55, 1 (2016), 31–38. (2016) 
  3. Konopleva, N. P., Popov, V. N., Kalibrovochnye polya, . Atomizdat, Moscow, 1972, (in Russian). (1972) 
  4. Lomsadze, Yu. M., Teoretiko-gruppovoe vvedenie v teoriyu elementarnykh chastits, . Vysshaia shkola, Moscow, 1962, (in Russian). (1962) 
  5. Burlakov, M. P., Evtushik, L. E., Clifford’s structure and Clifford’s differentiation on Riemann spaces, . Bull. Moscow Univ. – Math., Mech. 1, 2 (1994), 67–74, (in Russian). (1994) 

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