Supercommuting maps on unital algebras with idempotents

Yingyu Luo; Yu Wang; Yingyu Luo; Yu Wang

doi:10.3934/math.20241200

AIMS Mathematics

2024, Volume 9, Issue 9: 24636-24653. doi: 10.3934/math.20241200

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Research article

Supercommuting maps on unital algebras with idempotents

Yingyu Luo ¹,
Yu Wang ^{2
,
,}

1.
College of Mathematics, Changchun Normal University, Changchun 130032, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received: 29 June 2024 Revised: 10 August 2024 Accepted: 13 August 2024 Published: 22 August 2024
MSC : 15A78, 16W25, 17A70

Let $ \mathcal{A} $ be a unital algebra with nontrivial idempotents. We considered $ \mathcal{A} $ as a superalgebra according to Ghahramani and Zadeh's method. We provided a description of supercommuting maps on $ \mathcal{A} $. As a consequence, we gave a description of supercommuting maps on matrix algebras, which is different from the result on commuting maps of matrix algebras. Finally, we proved that every supercommuting map on triangular algebras is a commuting map.
- supercommuting map,
- commuting map,
- generalized matrix algebra,
- matrix algebra,
- triangular algebra
Citation: Yingyu Luo, Yu Wang. Supercommuting maps on unital algebras with idempotents[J]. AIMS Mathematics, 2024, 9(9): 24636-24653. doi: 10.3934/math.20241200

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Abstract

Let $ \mathcal{A} $ be a unital algebra with nontrivial idempotents. We considered $ \mathcal{A} $ as a superalgebra according to Ghahramani and Zadeh's method. We provided a description of supercommuting maps on $ \mathcal{A} $. As a consequence, we gave a description of supercommuting maps on matrix algebras, which is different from the result on commuting maps of matrix algebras. Finally, we proved that every supercommuting map on triangular algebras is a commuting map.

References

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