Unital decompositions of the matrix algebra of order three

Abstract

We classify all decompositions of $M_3(\mathbb{C})$ into a direct vector–space sum of two subalgebras such that one of the subalgebras contains the identity matrix.

Keywords:

• Sum of rings
• matrix algebra

2020MATHEMATICS SUBJECT CLASSIFICATION:

• 17B63

Acknowledgments

The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation.

Additional information

Funding

The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation.