Dynamical Reflection Maps
Ryosuke Ashikaga, Youichi Shibukawa
TL;DR
This paper introduces dynamical reflection maps using category theory, providing solutions to the reflection equation linked to dynamical Yang-Baxter maps and exploring quiver-theoretic solutions.
Contribution
It presents a novel categorical framework for dynamical reflection maps and extends the theory to quiver-theoretic solutions, advancing the mathematical understanding of these structures.
Findings
Constructed dynamical reflection maps via category theory.
Linked solutions to the reflection equation with dynamical Yang-Baxter maps.
Discussed quiver-theoretic solutions to the reflection equation.
Abstract
In this paper, by making use of category theory, we construct dynamical reflection maps, solutions to a version of the reflection equation associated with suitable dynamical Yang-Baxter maps, set-theoretic solutions to the braid relation that is equivalent to a version of the quantum Yang-Baxter equation. Quiver-theoretic solutions to the reflection equation are also discussed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra