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arXiv · 2308.16455

Nonunital decompositions of the matrix algebra of order three

Vsevolod Gubarev
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Abstract

All decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that none of the subalgebras contains the identity matrix are classified. Thus, the classification of all decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras as well as description of Rota-Baxter operators of nonzero weight on $M_3(\mathbb{C})$ is finished.

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Vsevolod Gubarev. 2023-08-31. Nonunital decompositions of the matrix algebra of order three. https://doi.org/10.32917/h2023008

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