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A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
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Fluxmetric and magnetometric demagnetizing factors, Nf and Nm, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ and the ratio γ of length to diameter. The results have an accuracy better than 0.1% with respect to min(Nf,m,1-Nf,m) and are tabulated in the range of 0.01?γ?500 and -1?χ<∞. Nm along the radial direction is evaluated with a lower accuracy from Nm along the axis and tabulated in the range of 0.01?γ?1 and -1?χ<∞. Some previous results are discussed and several applications are explained based on the new results. 相似文献
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We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Zp) gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n dimensional vector space which we call Hn. The Zp gauge particles act on the vertex particles and thus Hn can be thought of as a C(Zp) module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n and p, though we believe this feature holds for all n>p. We will see that non-Abelian anyons of the quantum double of C(S3) are obtained as part of the vertex excitations of the model with n=6 and p=3. Ising anyons are obtained in the model with n=4 and p=2. The n=3 and p=2 case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Zp. This makes them possible candidates for realizing quantum computation. 相似文献