A new set of generators and a physical interpretation for the \(SU (3)\) finite subgroup \(D(9, 1, 1;2, 1, 1)\)
نویسندگان
چکیده
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 [3], 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 JonesKauffman 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 Z9 × Z3 o S3 with respect to conjugation.
منابع مشابه
Finite groups with three relative commutativity degrees
For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if a...
متن کاملGeneral effective actions.
We investigate the structure of the most general actions with symmetry group G, spontaneously broken down to a subgroup H . We show that the only possible terms in the Lagrangian density that, although not G-invariant, yield G-invariant terms in the action, are in one to one correspondence with the generators of the fifth cohomology classes. For the special case of G = SU(N)L × SU(N)R broken do...
متن کاملGeometric and FurlctionM Analysis
We study the rate of convergence of symmetric random walks on finite groups to the uniform distribution. A notion of moderate growth is introduced that combines with eigenvalue techniques to give sharp results. Roughly, for finite groups of moderate growth, a random walk supported on a set of generators such that the diameter of the group is "f requires order ~ 2 steps to get close to the unifo...
متن کاملThe influence of S-embedded subgroups on the structure of finite groups
Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...
متن کاملOn the type of conjugacy classes and the set of indices of maximal subgroups
Let $G$ be a finite group. By $MT(G)=(m_1,cdots,m_k)$ we denote the type of conjugacy classes of maximal subgroups of $G$, which implies that $G$ has exactly $k$ conjugacy classes of maximal subgroups and $m_1,ldots,m_k$ are the numbers of conjugates of maximal subgroups of $G$, where $m_1leqcdotsleq m_k$. In this paper, we give some new characterizations of finite groups by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Quantum Information Processing
دوره 12 شماره
صفحات -
تاریخ انتشار 2013