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Full-Text Articles in Algebra
Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank
Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank
Faculty Journal Articles
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.