Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Classifying Lie Algebroid of a Geometric Structure II: G-structures with connection
265
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Given a G-structure with connection satisfying a regularity assumption we associate to it a classifying Lie algebroid. This algebroid contains all the information about the equivalence problem and is an example of a G-structure Lie algebroid. We discuss the properties of this algebroid, the G-structure groupoids integrating it and the relationship with Cartans realization problem.
rate research
Read More
We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartans realization problem that applies to both the local and the glob
We show that the compact quotient $Gammabackslashmathrm{G}$ of a seven-dimensional simply connected Lie group $mathrm{G}$ by a co-compact discrete subgroup $Gammasubsetmathrm{G}$ does not admit any exact $mathrm{G}_2$-structure which is induced by a left-invariant one on $mathrm{G}$.
We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed G$_2$-structures, up to isomorphism, and we show that six of them arise as the contactization of a symplectic Lie algebra. Finally, we prove that every semi-algebraic soliton on the contactization of a symplectic Lie algebra must be expanding, and we determine all unimodular Lie algebras with center of dimension at least two that admit semi-algebraic solitons, up to isomorphism.
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of extensions 0 --> L --> E --> Q --> 0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.
In this paper, we study the analytic continuation to complex time of the Hamiltonian flow of certain $Gtimes T$-invariant functions on the cotangent bundle of a compact connected Lie group $G$ with maximal torus $T$. Namely, we will take the Hamiltonian flows of one $Gtimes G$-invariant function, $h$, and one $Gtimes T$-invariant function, $f$. Acting with these complex time Hamiltonian flows on $Gtimes G$-invariant Kahler structures gives new $Gtimes T$-invariant, but not $Gtimes G$-invariant, Kahler structures on $T^*G$. We study the Hilbert spaces ${mathcal H}_{tau,sigma}$ corresponding to the quantization of $T^*G$ with respect to these non-invariant Kahler structures. On the other hand, by taking the vertical Schrodinger polarization as a starting point, the above $Gtimes T$-invariant Hamiltonian flows also generate families of mixed polarizations $mathcal{P}_{0,sigma}, sigma in {mathbb C}, {rm Im}(sigma) >0$. Each of these mixed polarizations is globally given by a direct sum of an integrable real distribution and of a complex distribution that defines a Kahler structure on the leaves of a foliation of $T^*G$. The geometric quantization of $T^*G$ with respect to these mixed polarizations gives rise to unitary partial coherent state transforms, corresponding to KSH maps as defined in [KMN1,KMN2].
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
