Structure and bimodules of simple Hom-alternative algebras
DOI:
https://doi.org/10.17398/2605-5686.36.1.1Keywords:
Bimodules, solvable, simple, Hom-alternative algebrasAbstract
This paper is mainly devoted to a structure study of Hom-alternative algebras. Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are provided. Moreover some results about Hom-alternative bimodule are found.
Downloads
References
B. Agrebaoui, K. Benali, A. Makhlouf, Representations of simple Hom-Lie algebras, J. Lie Theory 29 (4) (2019), 1119 – 1135.
S. Attan, H. Hounnon, B. Kpamegan, Hom-Jordan and Hom-alternative bimodules, Extracta Math. 35 (1) (2020), 69 – 97.
S. Benayadi, A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys. 76 (2014) 38 – 60.
X. Chen, W. Han, Classification of multiplicative simple Hom-Lie algebras, J. Lie Theory 26 (3) (2016) 767 – 775.
M. Elhamdadi, A. Makhlouf, Deformations of Hom-alternative and Hom-Malcev algebras, Algebras Groups Geom. 28 (2) (2011), 117 – 145.
J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra 295 (2) (2006), 314 – 361.
N. Jacobson, General representation theory of Jordan algebras, Trans. Amer. Math. Soc. 70 (1951), 509 – 530.
N. Jacobson, Structure of alternative and Jordan bimodules, Osaka Math. J. 6 (1954), 1 – 71.
D. Larsson, S.D. Silvestrov, Quasi-Hom-Lie algebras, Central Extensions and 2-cocycle-like identities, J. Algebra 288 (2) (2005), 321 – 344.
D. Larsson, S.D. Silvestrov, Quasi-Lie algebras, in “Noncommutative geometry and representation theory in mathematical physics”, Contemp. Math. 391, Amer. Math. Soc., Providence, RI, 2005, 241 – 248.
D. Larsson, S.D. Silvestrov, Quasi-deformations of sl2(F) using twisted derivations, Comm. Algebra 35 (12) (2007), 4303 – 4318.
X.X. Li, Structures of multiplicative Hom-Lie algebras, Adv. Math. (China) 43 (6) (2014), 817 – 823.
A. Makhlouf, Hom-alternative algebras and Hom-Jordan algebras, Int. Electron. J. Algebra 8 (2010), 177 – 190.
A. Makhlouf, S.D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2) (2008), 51 – 64.
R.D. Schafer, Alternative algebras over an arbitrary field, Bull. Amer. Math. Soc. 49 (1943), 549 – 555.
R.D. Schafer, Representations of alternative algebras, Trans. Amer. Math. Soc. 72 (1952), 1 – 17.
Y. Sheng, Representation of hom-Lie algebras, Algebr. Represent. Theory 15 (6) (2012), 1081 – 1098.
C. Yao, Y. Ma, L. Chen, Structures, classifications and bimodules of multiplicative simple Hom-Jordan algebras, arxiv:1906.04561v1.
D. Yau, Hom-algebras as deformations and homology, arxiv:0712.3515v1.
D. Yau, Hom-Maltsev, Hom-alternative and Hom-Jordan algebras, Int. Electron. J. Algebra 11 (2012), 177 – 217.
A. Zahari, A. Makhlouf Structure and classification of Hom-associative algebras, Acta Comment. Univ. Tartu. Math. 24 (1) (2020), 79 – 102.
M. Zorn, Theorie der alternativen Ringe, Abh. Math. Sem. Univ. Hamburg 8 (1) (1931), 123 – 147.
M. Zorn, Alternativkörper und quadratische Systeme, Abh. Math. Sem. Univ. Hamburg 9 (1) (1933), 395 – 402.
