Related papers: Homogeneous Symplectic Spaces and Central Extensio…

Let G be a group which is topologically a CW-complex, BG a classifying space for G, and A a discrete abelian group. To a central extension of G by A, one can associate a cohomology class in $H^2(BG,A)$. We show this association is…

We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…

In earlier work (*) we studied an extension of the canonical symplectic structure in the cotangent bundle of an affine space ${\cal Q}={\bf R}^N$, by additional terms implying the Poisson non-commutativity of both configuration and momentum…

The restricted Siegel disc is a homogeneous space related to the connected component $T_0(1)$ of the Universal Teichm\"uller space via the period mapping. In this paper we show that it is a coadjoint orbit of the universal central extension…

For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translation G-orbit is a totally real submanifold is induced from a…

In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We…

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…

Let $G$ be a simple complex Lie group, $\alg{g}$ be its Lie algebra, $K$ be a maximal compact form of $G$ and $\alg{k}$ be a Lie algebra of $K$. We denote by $X\rightarrow \overline{X}$ the anti-involution of $\alg{g}$ which singles out the…

We state conditions for which a definable local homomorphism between two locally definable groups $\mathcal{G}$, $\mathcal{G^{\prime}}$ can be uniquely extended when $\mathcal{G}$ is simply connected (Theorem 2.1). As an application of this…

In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain $\omega$ on a Lie algebra $h$ with values in an $h$-module $V$, we associate subalgebras $sp(h,\omega) \supeq…

We generalize the notion of kinematical Lie algebra introduced in physics for the classification of the various possible relativity algebras an isotropic spacetime can accommodate. We first give an elementary proof of the fact that such a…

Let $M$ be a $2n$-dimensional closed symplectic manifold admitting a Hamiltonian circle action with isolated fixed points. We show that if $M$ contains an $S^1$-invariant symplectic hypersurface $D$ such that $M\setminus D$ is a homology…

Let $M$ be a simply connected pseudo-Riemannian homogeneous space of finite volume with isometry group $G$. We show that $M$ is compact and that the solvable radical of $G$ is abelian and the Levi factor is a compact semisimple Lie group…

We show that generic symplectic quotients of a Hamiltonian $G$-space $M$ by the action of a compact connected Lie group $G$ are also symplectic quotients of the same manifold $M$ by a compact torus. The torus action in question arises from…

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…

We classify the finite type (in the sense of E. Cartan theory of prolongations) subalgebras $\mathfrak{h}\subset\mathfrak{sp}(V)$, where $V$ is the symplectic 4-dimensional space, and show that they satisfy $\mathfrak{h}^{(k)}=0$ for all…

Let $R := R_{2}(p)=\mathbb{C}[t^{\pm 1}, u : u^2 = t(t-\alpha_1)\cdots (t-\alpha_{2n})] $ be the coordinate ring of a nonsingular hyperelliptic curve and let $\mathfrak{g}\otimes R$ be the corresponding current Lie algebra. \color{black}…

The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a…

We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral algebraic K-theoretic (split) Novikov conjecture…