References

HOM-HYPOREDUCTIVE TRIPLE ALGEBRAS


[1] M. A. Akivis, Local differential quasigroups and 3-webs of multidimensional surfaces, In: Studies in the Theory of Quasigroups and Loops, Stiinta, Kishinev, Russian, 1973, 3-12.

[2] M. A. Akivis, Local algebras of a multidimensional 3-web, Siberian Mathematical Journal 17(7) (1976), 3-8.
DOI: https://doi.org/10.1007/BF00969285

[3] H. Ataguema, A. Makhlouf and S. D. Silvestrov, Generalization of n-ary Nambu algebras and beyond, Journal of Mathematical Physics 50(8) (2009); Article 083501.
DOI: https://doi.org/10.1063/1.3167801

[4] S. Attan and A. N. Issa, Hom-Bol algebras, Quasigroups and Related Systems 21(2) (2013), 131-146.

[5] D. Gaparayi and A. N. Issa, A twisted generalization of Lie-Yamaguti algebras, International Journal of Algebra 6(7) (2012), 339-352.

[6] E. G. Goodaire, Alternative rings of small order and the hunt for Moufang circle loops in Nonassociative Algebra and its Applications (São Paulo, 1998), vol. 211 of Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York, 2000, 137-146.

[7] J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using Journal of Algebra 295(2) (2006), 314-361.
DOI: https://doi.org/10.1016/j.jalgebra.2005.07.036

[8] I. R. Hentzel and L. A. Peresi, Special identities for Bol algebras, Linear Algebra and its Applications 436(7) (2012), 2315-2330.
DOI: https://doi.org/10.1016/j.laa.2011.09.021

[9] K. H. Hofmann and K. Strambach, Lie’s fundamental theorems for local analytical loops, Pacific Journal of Mathematics 123(2) (1986), 301-327.

[10] A. N. Issa, Hom-Akivis algebras, Commentationes Mathematicae Universitatis Carolinae 52(4) (2011), 485-500.

[11] A. N. Issa, Classifying two-dimensional hyporeductive triple algebras, International Journal of Mathematics and Mathematical Sciences, 2006, 1-10; Article ID 013527.
DOI: https://doi.org/10.1155/IJMMS/2006/13527

[12] A. N. Issa, On the theory of hyporeductive algebras, Algebraic Methods in Geometry (V. V. Ryzhkov, et al., Editors) Collect. Sci. Woorks, Izd. Ross. Univ. druzhby Narodov, Moskva, 1992, pp. 20-25.

[13] A. N. Issa, Notes on the geometry of smooth hyporeductive loops, Algebras, Groups and Geometries 12(3) (1995), 223-246.

[14] A. N. Issa, Remarks on the construction of Lie-Yamaguti algebras, International Journal of Algebra 5(14) (2011), 667-677.

[15] D. Larsson and S. D. Silvestrov, Quasi-Hom-Lie algebras, central extensions and 2-cycle-like identifies, Journal of Algebra 288(2) (2005), 321-344.
DOI: https://doi.org/10.1016/j.jalgebra.2005.02.032

[16] D. Larsson and S. D. Silvestrov, Quasi-Lie algebras, Contemporary Mathematics 391 (2005).

[17] W. G. Lister, A structure theory of Lie triple system, Transactions of the American Mathematical Society 72(2) (1952), 217-242.
DOI: https://doi.org/10.2307/1990753

[18] A. Makhlouf, Hom-alternative algebras and Hom-Jordan algebras, International Electronic Journal of Algebra 8 (2010), 177-190.

[19] A. Makhlouf and S. D. Silvestrov, Hom-algebra structures, Journal of Generalized Lie Theory and Applications 2(2) (2008), 51-64.

[20] P. O. Mikheev, Commutator algebras of right alternative algebras (Russian), Mat. Issled. 113 (1990), 62-65.

[21] P. O. Mikheev and L. V. Sabinin, Quasigroups and differential geometry, Quasigroups and Loops: Theory and Applications (O. Chein, H. O. Pflugfelder and J. D. H. Smith, Editors), Sigma Series in Pure Mathematics, Vol. 8, Heldermann, Berlin (1990), pp. 357-430.

[22] L. V. Sabini, On smooth hyporeductive loops, Soviet Mathematics, Doklady 42(2) (1991), 524-526.

[23] L. V. Sabini, Smooth Hyporeductive Loops, Webs and Quasigroups (Moscow, 1989), Tver. Gos. Univ., Tver, 1991, pp. 129-137.

[24] L. V. Sabini, The theory of smooth hyporeductive and pseudoreductive loops, Algebras, Groups and Geometries 13(1) (1996), 1-24.

[25] A. A. Sagle, Malcev algebras, Transactions of the American Mathematical Society 101(3) (1961), 426-458.
DOI: https://doi.org/10.1090/S0002-9947-1961-0143791-X

[26] K. Yamaguti, On the Lie triple system and its generalisation, Journal of Science of the Hiroshima University, Series A 21(3) (1958), 155-160.
DOI: https://doi.org/10.32917/hmj/1555639527

[27] D. Yau, Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras, International Electronic Journal of Algebras 11 (2012), 177-217.

[28] D. Yau, Hom-algebras and Homology, Journal of Lie Theory 19(2) (2009), 409-421.

[29] D. Yau, Hom-Novikov algebras, Journal of Physics A: Mathematical and Theoretical 44(8) (2011); Article 085202.
DOI: https://doi.org/10.1088/1751-8113/44/8/085202

[30] D. Yau, On n-ary Hom-Nambu and Hom-Nambu-Lie algebras, Journal of Geometry and Physics 62(2) (2012), 506-522.
DOI: https://doi.org/10.1016/j.geomphys.2011.11.006