Abstract
We describe the unital finite-dimensional simple nonconstant bimodules \( {\mathcal{W}} \) over the matrix algebra \( M_{2}(F) \) over a field \( F \) of characteristic \( 0 \); i.e., the left action of the idempotents of \( M_{2}(F) \) is diagonalizable and \( {\mathcal{W}} \) does not contain constant bichains. Also, we construct an example of a nondiagonal bimodule and a series of constant right-symmetric bimodules over \( M_{2}(F) \).
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Acknowledgment
The author is grateful to the referee for the remarks that improve exposition.
Funding
Research was supported by the Russian Science Foundation (Project no. 21–11–00286).
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 2, pp. 392–403. https://doi.org/10.33048/smzh.2022.63.210
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Pozhidaev, A.P. On Nonconstant Pre-Lie Bimodules over \( M_{2}(F) \). Sib Math J 63, 326–335 (2022). https://doi.org/10.1134/S0037446622020100
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DOI: https://doi.org/10.1134/S0037446622020100