Abstract
Suppose that G is a finite group and D(G) the quantum double algebra of G. Let A be the field algebra of G-spin models. There is a natural action of D(G) on A such that A becomes a D(G)-module algebra. For a subgroup H of G, there is a Hopf subalgebra D(G;H) of D(G). Based on the concrete construction of a D(G;H) fixed point subalgebra, the paper proves that D(G;H) is Galois closed and thus gives a quantum Galois theory in the field algebra of G-spin models.
| Original language | English |
|---|---|
| Pages (from-to) | 2793-2801 |
| Number of pages | 9 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 138 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2010 |
Keywords
- Field algebra
- G-spin models
- Galois closed
- Hopf algebra
- Quantum double
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Lining, J. (2010). Towards a quantum galois theory for quantum double algebras of finite groups. Proceedings of the American Mathematical Society, 138(8), 2793-2801. https://doi.org/10.1090/S0002-9939-10-10315-3