Alphabeta MathFinite-group Hopf algebra and lattice quantum-double sectors
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1 · Prerequisites
- Absolute and Conditional Convergence; Rearrangement; Products
- Algebraic Closure, Embeddings, and Separability
- Algebraic Extensions, Extension Degree, and Finite Fields
- Analyticity of Holomorphic Functions; Liouville and Morera
- Approximation and Compactness in C(K)
- Arc Length and Rectifiable Curves
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2 · Logical flowchart
3 · Items
Definition
Explicit finite-group quantum-double data
Theorem
Hopf-* structure of the finite-group double
Definition
Oriented finite-group lattice gauge operators
Theorem
Gauge averaging and flatness commute
Lemma
Squared finite-group irreducible dimensions sum to the group order
Theorem
Irreducible sectors of the finite-group double
Sources
- A. Yu. Kitaev, Fault-tolerant quantum computation by anyons
- Mark de Wild Propitius and F. Alexander Bais, Discrete Gauge Theories
- Alexander Cowtan and Shahn Majid, Quantum Double Aspects of Surface Code Models
- Peter Webb, A Course in Finite Group Representation Theory
- Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina, Introduction to Representation Theory