Classification of indecomposable involutive set-theoretic solutions to the Yang–Baxter equation
Wolfgang Rump
Abstract
Abstract Using the theory of cycle sets and braces, non-degenerate indecomposable involutive set-theoretic solutions to the Yang–Baxter equation are classified in terms of their universal coverings and their fundamental group. The universal coverings are characterized as braces with an adjoint orbit generating the additive group. Using this description, all coverings of non-degenerate indecomposable cycle sets are classified. The method is illustrated by examples.
Topics & Concepts
Indecomposable moduleMathematicsDegenerate energy levelsPure mathematicsSet (abstract data type)Yang–Baxter equationGroup (periodic table)Algebra over a fieldComputer scienceQuantum mechanicsQuantumProgramming languagePhysicsAdvanced Topics in AlgebraAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic Topology