On the Lie Centralizers of Quaternion Rings
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Authors: M. A. BAHMANI AND F. GHOMANJANI
DOI: 10.46793/KgJMat2203.471B
Abstract:
In this paper, we investigate the problem of describing the form of Lie centralizers on quaternion rings. We provide some conditions under which a Lie centralizer on a quaternion ring is the sum of a centralizer and a center valued map.
Keywords:
Centralizer, Lie centralizer, quaternion ring.
References:
[1] S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, New York, 1995.
[2] O. P. Agrawal, Hamilton operators and dual-number-quaternions in spatial kinematics, Mechanism and Machine Theory 22(6) (1987), 569–575.
[3] A. Fošner and W. Jing, Lie centralizers on triangular rings and nest algebras, Adv. Oper. Theory 4 (2019), 342–350.
[4] H. Ghahramani, M. N. Ghosseiri and L. Heidari Zade, On the Lie derivations and generalized Lie derivations of quaternion rings, Comm. Algebra 47(3) (2019), 1215–1221.
[5] H. Ghahramani, M. N. Ghosseiri and S. Safari, Some questions concerning superderivations on ℤ2-graded rings, Aequationes Math. 91(4) (2017), 725–738.
[6] F. Ghomanjani and M. A. Bahmani, A note on Lie centralizer maps, Palest. J. Math. 7(2) (2018), 468–471.
[7] B. Hvala, Generalized Lie derivations in prime rings, Taiwanese J. Math. 11(5) (2007), 1425–1430.
[8] M. Jafari and Y. Yayli, Generalized quaternions and their algebraic properties, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 64(1) (2015), 15–27.
[9] W. Jing, Additivity of Lie centralizers on triangular rings, Math and Computer Science Working Papers (2011), 1–10.
[10] B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), 609–614.