Nonunital decompositions of the matrix algebra of order three

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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Cited by in corpus (3)

• Rota-Baxter operators on the simple Jordan algebra of matrices of order two
• Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra
• Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel