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Z2×Z2 lattice as a Connes–Lott-quantum group model

✍ Scribed by Shahn Majid; Thomas Schücker

Book ID
104343103
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
205 KB
Volume
43
Category
Article
ISSN
0393-0440

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✦ Synopsis

We apply quantum group methods for noncommutative geometry to the Z 2 × Z 2 lattice to obtain a natural Dirac operator on this discrete space. This then leads to an interpretation of the Higgs fields as the discrete part of space-time in the Connes-Lott formalism for elementary particle Lagrangians. The model provides a setting where both the quantum groups and the Connes approach to noncommutative geometry can be usefully combined, with some of Connes' axioms, notably the first-order condition, replaced by algebraic methods based on the group structure. The noncommutative geometry has nontrivial cohomology and moduli of flat connections, both of which we compute.

📜 SIMILAR VOLUMES

Problem 144.: Is the following conjectur
Problem 144.: Is the following conjecture true? Conjecture: If G is a simple group, then γ(Z2×G)=σ(Z2×G).
📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 50 KB

Problem 142. The symmetric genus of a group G is the minimum genus of a surface on which G acts. Let A, denote the alternating group of degree n, y(G) denote the genus of the group G, and a(G) the symmetric genus of G. Is the following conjecture true? Conjecture: For at least one n, y(A,l) c a(A,,)