This structure-preserving factorization of the symplectic matrices immediately reveals two well-known features that (i) the determinant of any symplectic matrix is one and (ii) the matrix symplectic group is path connected, as well as a new feature that (iii) all the unit triangular symplectic ...
Let G be a Lie group which integrates the Lie algebra g. Regarding the commutator (1.1) as coming from the quantization of a linear Poisson bracket on X, one can integrate the latter to a symplectic groupoid. This is given by the cotangent bundle T ∗G with its canonical symplectic ...
Symplectic matrices form a connected Lie group. Hamiltonian flows consist of symplectomorphisms. Gromov's theorem shows that Hamiltonian flows preserve symplectic capacities. This leads to a topological version of Heisenberg's uncertainty principle in classical mechanics. It also leads to a topological ...
It is proved that any harmonic map (?): Ω→Sp(N) from a simply connected domain Ω (?) R2∪ {∞} into the symplectic group Sp(N)(?)U(2N) with finite unito... Q He,Y Shen - 《中国科学:数学(英文版)》 被引量: 44发表: 2001年 Maximal subgroups of symplectic groups stabilizing...
For a geometer, at least under some assumptions on the manifold M, this is just the connected component of the identity in the group of all symplectic diffeomorphisms. From the viewpoint of mechanics, Ham(M,O) is the group of all admissible motions. What is the minim...
LetXbeacompactclosedorientedsimplyconnectedtopological4-manifold,andGbea finitegroup.Whenstudyingactionsonmanifoldofafinitegroup,onecanconsideraninduced actiononsomealgebraicinvariantsassociatedwiththemanifold,anditisoftenimportantand beneficia1.~ rthermore,acentralproblemistodescribethestructureofthefixedpointset ...
a group with several parameters, implies several first integrals. The phase flow is therefore confined to the intersection of the level surfaces of these integrals: an intersection which is in general a manifold. In other words: the simultaneous level manifold of these integrals is an invariant ...
In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded ...
The quiver is SO(13) G2 Sp(1) −3 −1 (2.13) which is similar to (2.12) except that in F-theory the Sp(1) is supported on a (−1)-curve and the G2 is supported on a (−3)-curve. There are two tensor multiplets associated to each gauge group. The (−1)-curve ...
The set of linearly independent closed 2-forms which cannot be expressed as.dA for some 1-form.A is the second cohomology group of the manifold .M; this is denoted by .H2(M).1 Thus, if the phase space .M has nontrivial second cohomology, i.e., if .H2(M) /= 0, then there ...