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arXiv · 1812.00275

Exact sequences of inner automorphisms of tensors

Peter A. Brooksbank·Joshua Maglione·James B. Wilson
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Abstract

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner similar to those, our sequence facilitates inductive reasoning about, and calculation of the groups of symmetries of a tensor. The new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics.

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Peter A. Brooksbank, Joshua Maglione, James B. Wilson. 2019-07-06. Exact sequences of inner automorphisms of tensors. https://doi.org/10.1016/j.jalgebra.2019.07.006

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