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Pré-Publication, Document De Travail Année : 2022

Jordan Decompositions of Tensors

Résumé

We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra which acts on it and embed them into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information.

Dates et versions

hal-03720101 , version 1 (11-07-2022)

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Citer

Frederic Holweck, Luke Oeding. Jordan Decompositions of Tensors. 2022. ⟨hal-03720101⟩
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