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DUALISTIC STRUCTURE ON ALMOST COSYMPLECTIC HOM-LIE ALGEBRAS
Keywords:
almost cosymplectic structure, Hom-Lie group, Hom-Lie algebra, Hom-Levi-Civita connection.DOI:
https://doi.org/10.17654/0972555524005Abstract
We investigate almost cosymplectic statistical structure on Hom-Lie algebra and provide some of its curvature properties. Examples are also provided in order to clarify the results obtained.
Received: November 2, 2023
Accepted: December 20, 2023
References
S. Amari, Differential-geometrical methods in statistics, Lecture Notes in Statistics, Springer-Verlag, Berlin/Heidelberg, Vol. 28, 1985.
S. Amari and H. Nagaoka, Methods of information geometry, Transl. Math. Monogr. 191, Amer. Math. Soc., 2000.
F. Ammar, Z. Ejbehi and A. Makhlouf, Cohomology and deformations of Hom-algebras, J. Lie Theory 21 (2011), 813-836.
S. Beneyadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Math. Phys. 76 (2014), 38-60.
S. Caenepeel and I. Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Algebra 39 (2011), 2216-2240.
J. Hartwing, D. Larson and S. Sylvestrov, Deformation of Lie algebras using sigma-derivations, J. Algebra 295 (2006), 314-361.
J. Hu, q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq. 6(1) (1999), 51-70.
C. Laurent-Gengoux, C. Makhlouf and A. Teles, Universal algebra of a Hom-Lie algebra and group-like elements, J. Pure Appl. Algebra 222(5) (2018), 1139-1163.
K. E. Irem, M. Cengizhan and Y. Aziz, Almost cosymplectic statistical manifolds, Quaest. Math. 43 (2020), 265-282. DOI: 10.2989/16073606.2019.1576069.
J. Jiang, S. K. Mishra and Y. Sheng, Hom-Lie algebras and Hom-Lie groups, integration and differentiation, SIGMA 16(22) (2020), 627-649.
A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2(2) (2008), 51-64.
M. Noguchi, Geometry of statistical manifolds, Differential Geom. Appl. 2 (1992), 197-222.
E. Peyghan, L. Nourmohammadifar, A. Makhlouf and A. Gezer, Kahler-Norden structures on Hom-Lie groups and Hom-Lie algebras.
arXiv:2002.03436v1 [math.DG] 9 Feb 2020.
E. Peyghan and L. Nourmohammadifar, Para-Kahler Hom-Lie algebras, J. Algebra Appl. 18(3) (2019), 1950044, 24 pp.
E. Peyghan and L. Nourmohammadifar, Almost contact Hom-Lie algebras and Sasakian Hom-Lie algebras, J. Algebra Appl. 21(1) (2022), 2250005, 27 pp.
E. Peyghan, L. Nourmohammadifar, A. Gezer and E. Tosun, CoKahler and cosymplectic Hom-Lie Algebras, Mediterr. J. Math. 20(2) (2023), 1-26.
Y. Sheng, Representations of Hom-Lie algebras, Algebr. Represent. Theor. 15 (2012), 1081-1098.
D. Yau, Hom algebras and homology, J. Lie Theory 19 (2009), 409-421.
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