共查询到20条相似文献,搜索用时 562 毫秒
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V.I. Arnold [V. I. Arnold, Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane, Journal of Geometry and Physics, 53 (4) (2005), 421–427] gave an alternative proof to the Lobachevsky triangle altitudes theorem by using a Poisson bracket for quadratic forms and its Jacobi identity, and showed that the orthocenter theorem can be extended on RP2. In this paper, we find a new identity in the Poisson algebra of quadratic forms. Following Arnold’s idea, the goal of this article is to give alternative proofs to theorems, of Desargues, Pascal, and Brianchon, in RP2, by using the Poisson bracket and the identity. 相似文献
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We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z2)n-graded commutative associative algebra A. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonné determinant of quaternionic matrices, but in general our quaternionic determinant is different. We show that the graded determinant of purely even (Z2)n-graded matrices of degree 0 is polynomial in its entries. In the case of the algebra A=H of quaternions, we calculate the formula for the Berezinian in terms of a product of quasiminors in the sense of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and determinant) by a (Z2)n-graded version of Liouville’s formula. 相似文献
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We present explicit constructions of complete Ricci-flat Kähler metrics that are asymptotic to cones over non-regular Sasaki–Einstein manifolds. The metrics are constructed from a complete Kähler–Einstein manifold (V,gV) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kähler metrics on the total spaces of (i) holomorphic C2/Zp orbifold fibrations over V, (ii) holomorphic orbifold fibrations over weighted projective spaces WCP1, with generic fibres being the canonical complex cone over V, and (iii) the canonical orbifold line bundle over a family of Fano orbifolds. As special cases, we also obtain smooth complete Ricci-flat Kähler metrics on the total spaces of (a) rank two holomorphic vector bundles over V, and (b) the canonical line bundle over a family of geometrically ruled Fano manifolds with base V. When V=CP1 our results give Ricci-flat Kähler orbifold metrics on various toric partial resolutions of the cone over the Sasaki–Einstein manifolds Yp,q. 相似文献
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Let M be a connected complex projective manifold such that c1(T(1,0)M)=0. If M admits a holomorphic Cartan geometry, then we show that M is holomorphically covered by an abelian variety. 相似文献
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J.M. Ancochea Bermúdez R. Campoamor-Stursberg L. García Vergnolle 《Journal of Geometry and Physics》2011
The whole class of complex Lie algebras g having a naturally graded nilradical with characteristic sequence c(g)=(dimg−2,1,1) is classified. It is shown that up to one exception, such Lie algebras are solvable. 相似文献
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Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z2-symmetric toric code, SO(2N)1 and SU(3)1 state as well as the S3-symmetric SO(8)1 state and a non-Abelian chiral state we call the “4-Potts” state. 相似文献
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A family of spherically symmetric solutions with horizon in the model with m -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1 Ricci-flat “internal” spaces. The equation of state for any s -th component is defined by a vector Us belonging to Rn+1. The solutions are governed by moduli functions Hs obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M2–M5 configuration (in D=11 supergravity) corresponding to Lie algebra A2 is presented. 相似文献
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We study the partition function of two versions of the continuum directed polymer in 1+1 dimension. In the full-space version, the polymer starts at the origin and is free to move transversally in R, and in the half-space version, the polymer starts at the origin but is reflected at the origin and stays in R−. The partition functions solve the stochastic heat equation in full-space or half-space with mixed boundary condition at the origin; or equivalently the free energy satisfies the Kardar–Parisi–Zhang equation. 相似文献
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We propose methods towards a systematic determination of d -dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids Hn+1 and compact spheres Sn or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on S1×Sn, with n<6. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres Sd if d>5 (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification. 相似文献
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We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. 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
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We consider an extension of the standard model (SM) with three SU(2) scalar doublets and discrete S3⊗Z2 symmetries. The irreducible representation of S3 has a singlet and a doublet, and here we show that the singlet corresponds to the SM-like Higgs and the two additional SU(2) doublets forming a S3 doublet are inert. In general, in a three scalar doublet model, with or without S3 symmetry, the diagonalization of the mass matrices implies arbitrary unitary matrices. However, we show that in our model these matrices are of the tri-bimaximal type. We also analyzed the scalar mass spectra and the conditions for the scalar potential is bounded from below at the tree level. We also discuss some phenomenological consequences of the model. 相似文献
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Any elliptic curve can be realised in the tangent bundle of the complex projective line as a double cover branched at four distinct points on the zero section. Such a curve generates, via classical osculation duality, a null curve in C3 and thus an algebraic minimal surface in R3. We derive simple formulae for the coordinate functions of such a null curve. 相似文献
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We study, following Bertini et al. [1], the hidden conformal symmetry of the massless Klein–Gordon equation in the background of the general, charged, spherically symmetric, static black-hole solution of a class of d -dimensional Lagrangians which includes the relevant parts of the bosonic Lagrangian of any ungauged supergravity. We find that a hidden SL(2,R) symmetry appears at the near event- and Cauchy-horizon limits. We extend the two sl(2) algebras to two full Witt algebras (Virasoro algebras with vanishing central charges). We comment on the implications of the possible existence of an associated quantum conformal field theory. 相似文献