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MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I

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CramerZ MarcouxLW RadjaviH 2021 Matrix algebras with a certain compression property I - preprint.pdf (412.87 KB)

Date

2021-07-15

Authors

Cramer, Zachary
Marcoux, Laurent W.
Radjavi, Heydar

Journal Title

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Volume Title

Publisher

Elsevier

Abstract

An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all idempotents E in Mn(C). In this paper we construct several examples of unital algebras that admit these properties. In addition, a complete classification of the unital idempotent compressible subalgebras of M3(C) is obtained up to similarity and transposition. It is shown that in this setting, the two notions of compressibility agree: a unital subalgebra of M3(C) is projection compressible if and only if it is idempotent compressible. Our findings are extended to algebras of arbitrary size in [2]

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2021.03.005. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license

Keywords

compression, projection compressibility, idempotent compressibility, algebraic corners

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Citation

URI

https://doi.org/10.1016/j.laa.2021.03.005
 http://hdl.handle.net/10012/18252

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Waterloo Research
Pure Mathematics