Dispersing representations of semi-simple subalgebras of complex matrices
| dc.contributor.author | Marcoux, Laurent W. | |
| dc.contributor.author | Radjavi, Heydar | |
| dc.contributor.author | Zhang, Yuanhang | |
| dc.date.accessioned | 2022-05-16 20:35:58 (GMT) | |
| dc.date.available | 2022-05-16 20:35:58 (GMT) | |
| dc.date.issued | 2022-06-01 | |
| dc.identifier.uri | https://doi.org/10.1016/j.laa.2022.02.017 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18284 | |
| dc.description | The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2022.02.017 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license | en |
| dc.description.abstract | In this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semi-simple subalgebras of the set Mn of n⇥n complex matrices, and P 2 M2n is a projection of rank n. We exhibit a number of equivalent formulations of this problem, including the one which occupies the majority of the paper, namely: determine the minimum dimension of the space A\ S−1BS, where S is allowed to range over the invertible group GL(n,C) of Mn. This problem in turn is seen to be equivalent to the problem of finding two automorphisms ↵ and " of Mn for which the dimension of ↵(A)+"(B) is maximised. It is this phenomenon which gives rise to the title of the paper. | en |
| dc.description.sponsorship | Research supported in part by NSERC (Canada). Research supported in part by National Natural Science Foundation of China (No.: 12071174), Science and Technology Development Project of Jilin Province (No.: 20190103028JH). | en |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | maximal off-diagonal dimension | en |
| dc.subject | minimal intersection | en |
| dc.subject | semi-simple subalgebras of matrix algebras | en |
| dc.subject | dispersion | en |
| dc.title | Dispersing representations of semi-simple subalgebras of complex matrices | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Marcoux, L. W., Radjavi, H., & Zhang, Y. (2022). Dispersing representations of semi-simple subalgebras of complex matrices. Linear Algebra and Its Applications, 642, 160–220. https://doi.org/10.1016/j.laa.2022.02.017 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.typeOfResource | Text | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
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