Classification of connected \'etale algebras in pre-modular fusion categories up to rank three
Ken Kikuchi

TL;DR
This paper classifies connected étale algebras in pre-modular fusion categories of rank up to three, providing insights into their structure, Lagrangian algebras, and implications for ground state degeneracy and symmetry breaking in physics.
Contribution
It offers a complete classification of connected étale algebras in low-rank pre-modular fusion categories, including degenerate and non-(pseudo-)unitary cases, with applications to physics.
Findings
Classification of algebras up to rank three
Analysis of Lagrangian algebras and their properties
Implications for ground state degeneracy and symmetry breaking
Abstract
We classify connected \'etale algebras 's in pre-modular fusion categories with including degenerate and non-(pseudo-)unitary ones. We comment on Lagrangian algebras and physical applications to ground state degeneracy and proof of spontaneous -symmetry breaking.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra
