Duality between $p$-groups with three characteristic subgroups and semisimple anti-commutative algebras

Glasby, S. P.; Ribeiro, Frederico Augusto Menezes; Schneider, Csaba

doi:10.48550/arxiv.1711.04998

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2020

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“…We consider the Tensor Isomorphism Problem (TIP), which essentially asks whether two grids of numbers are equivalent up to change of basis. The problem arises in areas ranging from classifications of algebraic structures [4,5,10,16] to computational complexity [14,17] to quantum phases of matter [8,19]. Previous attacks on the problem also exploit ideas from a variety of areas, including * -algebras, Lie and Jordan algebras, numerical methods, and invariant theory.…”

Section: Introductionmentioning

confidence: 99%

Tensor Isomorphism by conjugacy of Lie algebras

Brooksbank,

Maglione,

Wilson

2020

Preprint

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We introduce an isomorphism test for structures having a distributive type property, such as tensors, rings, and nilpotent groups. The test applies a universal construction to generalize several existing isomorphism tests, recovering these as special cases. Whereas earlier methods exploit associative algebras and their representations, the new approach is based on Lie algebras, leading to polynomial-time isomorphism tests for new families.

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