Representation up to Homotopy and Hom-Lie Algebroid Modules

Merati, S.; Farhangdoost, Mohammad Reza; Attari Polsangi, A.R.

doi:10.1080/1726037X.2020.1788817

Journal of Dynamical Systems and Geometric Theories

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Open Access Research Article

Representation up to Homotopy and Hom-Lie Algebroid Modules

S. Meratis.merati@shirazuac.irDepartment of MathematicsCollege of SciencesShiraz UniversityShiraz, P.O. Box 71457-44776, IranView full profile → , ^*Mohammad Reza FarhangdoostCorresponding authorfarhang@shirazu.ac.irDepartment of MathematicsCollege of SciencesShiraz UniversityShiraz, P.O. Box 71457-44776, IranView full profile → , A.R. Attari PolsangiDepartment of MathematicsCollege of SciencesShiraz UniversityShiraz, P.O. Box 71457-44776, IranView full profile →

* Corresponding author · click or hover a name for details

pp. 27–37Vol. 18Issue 1January 2020DOI: 10.1080/1726037X.2020.1788817XML

Received:: 10 May 2019
Accepted:: 25 Jul 2019
Published Online:: 29 Jul 2020
Article type:: Research Article
Language:: EN
Article no.:: 1726037X.2020.1788817
Pages:: 27–37

Abstract

In this paper we introduce the concept of hom-Lie algebroid modules and hom-Lie algebroids. Then we show the correspondence between hom-Lie algebroid modules and representation up to homotopy of hom-Lie algebroids. Because of the effective role of representation theory and Lie algebraic structures in particle physics, we show the correspondence between bi-graded hom-Lie algebraic modules and hom-Lie algebraist. At the end, we study some properties of representation up to homotopy, using the language of hom-Lie algebroid modules.

Keywords

Hom-Lie algebroidsRepresentation up to homotopySuperconnectionChern-Weil forms

Subject Classifications

20L0522A2218D05

References

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Cite this article

S. Merati, M. R. Farhangdoost, and A. Attari Polsangi, "Representation up to Homotopy and Hom-Lie Algebroid Modules," Journal of Dynamical Systems and Geometric Theories, vol. 18, no. 1, pp. 27–37, 2020, doi: 10.1080/1726037X.2020.1788817.

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[1] C. A.Abad, M.Crainic. , J. reine angew. Math ., 663 , 91 - 126 ( 2012 ).

[2] M.Crainic, R. L.Fernandes. , Geom. Topol. Monogr ., 17 , 1 - 107 ( 2011 ).

[3] T.Drummond, M.Jotz Lean, C.Ortiz. . Diff. Geom. Appl ., 40 , 332 - 357 ( 2015 ). doi: 10.1016/j.difgeo.2015.03.005

[4] C.Laurent-Gengoux, J.Teles. , J. Geom. Phys. , 68 , 69 - 75 (2013). doi: 10.1016/j.geomphys.2013.02.003

[5] K. C. H.Mackenzie. , Adv. Math ., 94 ( 2 ), 180 - 239 ( 1992 ). doi: 10.1016/0001-8708(92)90036-K

[6] K. C. H.Mackenzie. , Adv. Math ., 154 , 46 - 75 ( 2000 ). doi: 10.1006/aima.1999.1892

[7] R. A.Mehta. , Indag. Math ., 25 , 1122 - 1134 ( 2014 ). doi: 10.1016/j.indag.2014.07.013

[8] S.Merati, M. R.Farhangdoost. , J. Algebra Appl ., ( 2018 ).

[9] S.Merati, M. R.Farhangdoost. , Int. J. Geom. Methods Mod. Phys ., ( 2018 ).

[10] S.Merati, M. R.Farhangdoost. , DSGT , 16 , 89 - 99 ( 2017 ).

[11] A. Yu.Vaĭntrob. , Uspekhi Mat. Nauk ., 52 (2( 314 )), 161 - 162 ( 1997 ). doi: 10.4213/rm831