A new set of generators and a physical interpretation for the $$SU (3)$$ finite subgroup $$D(9,1,1;2,1,1)$$

A new set of generators and a physical interpretation for the $$SU (3)$$ finite subgroup... After 100 years of effort, the classification of all the finite subgroups of $$SU(3)$$ is yet incomplete. The most recently updated list can be found in Ludl (J Phys A Math Theory 44:255204, 2011), where the structure of the series $$(C)$$ and $$(D)$$ of $$SU(3)$$ -subgroups is studied. We provide a minimal set of generators for one of these groups which has order $$162$$ . These generators appear up to phase as the image of an irreducible unitary braid group representation issued from the Jones–Kauffman version of $$SU(2)$$ Chern–Simons theory at level $$4$$ . In light of these new generators, we study the structure of the group in detail and recover the fact that it is isomorphic to the semidirect product $$\mathbb Z _9\times \mathbb Z _3\rtimes S_3$$ with respect to conjugation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

A new set of generators and a physical interpretation for the $$SU (3)$$ finite subgroup $$D(9,1,1;2,1,1)$$

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Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0544-6
Publisher site
See Article on Publisher Site

Abstract

After 100 years of effort, the classification of all the finite subgroups of $$SU(3)$$ is yet incomplete. The most recently updated list can be found in Ludl (J Phys A Math Theory 44:255204, 2011), where the structure of the series $$(C)$$ and $$(D)$$ of $$SU(3)$$ -subgroups is studied. We provide a minimal set of generators for one of these groups which has order $$162$$ . These generators appear up to phase as the image of an irreducible unitary braid group representation issued from the Jones–Kauffman version of $$SU(2)$$ Chern–Simons theory at level $$4$$ . In light of these new generators, we study the structure of the group in detail and recover the fact that it is isomorphic to the semidirect product $$\mathbb Z _9\times \mathbb Z _3\rtimes S_3$$ with respect to conjugation.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 23, 2013

References

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