Related papers: Real structures on symmetric spaces

We study the integrability of a (almost) complex structure calibrated by a symplectic form. We find new sufficent conditions.

We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case.

We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism class of their absolute Galois groups. Our results concern two cases: saturated PAC structures and non-saturated…

We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real…

With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties…

We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states.…

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S^{m-1}_R$ of large enough radius $R$. We obtain new classes of real polynomial maps $\mathbb R^m \to \mathbb…

If there exists a set of canonical classes on a compact Hamiltonian-$T$-spaces in the sense of Goldin and Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the…

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, \omega), where \gk is an appropriate regular subalgebra of…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

Let $X$ be a connected complex manifold equipped with a holomorphic action of a complex Lie group $G$. We investigate conditions under which a principal bundle on $X$ admits a $G$--equivariance structure.

We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant partially complex structure, or $f$-structure, introducing the notion of (almost) K\"ahler--Poisson manifolds. In…

We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumptions, we show the existence of a well-behaved chamber structure…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

We construct the odd symplectic structure and the equivariant even (pre)symplectic one from it on the space of differential forms on the Riemann manifold. The Poincare -- Cartan like invariants of the second structure define the equivariant…

Given an algebraic structure on the homology of a chain complex, we define its realization space as a Kan complex whose vertices are the structures up to homotopy realizing this structure at the homology level. Our algebraic structures are…

Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we…

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves…

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…

We explore the relationship between limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit space admits a self-similar structure, and also the condition…