Pseudorepresentations not arising from genuine representations

We show that a pseudorepresentation \(\textbf{D}\colon A[G] \to A\) of a (finite) group \(G\) need not arise from a genuine representation, even if one is allowed to extend the ring \(A\). This shows that a theorem of the "embedding problem" for residually multiplicity free pseudorepresent...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Author: Luo, Jinyue
Format: Article
Language:English
Subjects:
Representations
Online Access:Get full text
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Summary:We show that a pseudorepresentation \(\textbf{D}\colon A[G] \to A\) of a (finite) group \(G\) need not arise from a genuine representation, even if one is allowed to extend the ring \(A\). This shows that a theorem of the "embedding problem" for residually multiplicity free pseudorepresentations can not be extended to the general setting.
ISSN:2331-8422