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This content will become publicly available on March 31, 2025

Title: A Scale-Invariant Relaxation in Low-Rank Tensor Recovery with an Application to Tensor Completion
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Author(s) / Creator(s):
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Date Published:
Journal Name:
SIAM Journal on Imaging Sciences
Page Range / eLocation ID:
756 to 783
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Abstract The problem of whether the cohomological support map of a finite dimensional Hopf algebra has the tensor product property has attracted a lot of attention following the earlier developments on representations of finite group schemes. Many authors have focused on concrete situations where positive and negative results have been obtained by direct arguments. In this paper we demonstrate that it is natural to study questions involving the tensor product property in the broader setting of a monoidal triangulated category. We give an intrinsic characterization by proving that the tensor product property for the universal support datum is equivalent to complete primeness of the categorical spectrum. From these results one obtains information for other support data, including the cohomological one. Two theorems are proved giving compete primeness and non-complete primeness in certain general settings. As an illustration of the methods, we give a proof of a recent conjecture of Negron and Pevtsova on the tensor product property for the cohomological support maps for the small quantum Borel algebras for all complex simple Lie algebras. 
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