Search results for "Invariant"
showing 10 items of 783 documents
On exotic affine 3-spheres
2014
Every A 1 \mathbb {A}^{1} -bundle over A ∗ 2 , \mathbb {A}_{\ast }^{2}, the complex affine plane punctured at the origin, is trivial in the differentiable category, but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of such algebraic bundles are considered; in particular, the complex affine 3 3 -sphere S C 3 , \mathbb {S}_{\mathbb {C}}^{3}, given by z 1 2 + z 2 2 + z 3 2 + z 4 2 = 1 , z_{1}^{2}+z_{2}^{2}+z_{3}^{2}+z_{4}^{2}=1, admits such a structure with an additional homogeneity property. Total spaces of nontrivial homogeneous A 1 \mathbb {A}^{1} -bundles over A ∗ 2 \mathbb {A}_{\ast }^{2} are classified up to G m \mathbb {G}_{m}…
Actions and Invariant Character Degrees
1993
point subgroup. In general, we use the same notation as in 6 and 7 .wx wxPart of the proof of Theorem A depends on the basic properties of theGajendragadkar p-special characters 1 and we assume the reader iswxfamiliar with those. However, we will repeatedly use a deeper fact: anirreducible character a of a Hall p-subgroup
Invariant Markov semigroups on quantum homogeneous spaces
2019
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …
On cobordism of manifolds with corners
2000
This work sets up a cobordism theory for manifolds with corners and gives an identication with the homotopy of a certain limit of Thom spectra. It thereby creates a geometrical interpretation of Adams-Novikov resolutions and lays the foundation for investigating the chromatic status of the elements so realized. As an application Lie groups together with their left invariant framings are calculated by regarding them as corners of manifolds with interesting Chern numbers. The work also shows how elliptic cohomology can provide useful invariants for manifolds of codimension 2.
A group invariant Bishop-Phelps theorem
2021
We show that for any Banach space and any compact topological group G ⊂ L ( X ) G\subset L(X) such that the norm of X X is G G -invariant, the set of norm attaining G G -invariant functionals on X X is dense in the set of all G G -invariant functionals on X X , where a mapping f f is called G G -invariant if for every x ∈ X x\in X and every g ∈ G g\in G , f ( g ( x ) ) = f ( x ) f\big (g(x)\big )=f(x) . In contrast, we show also that the analog of Bollobás result does not hold in general. A version of Bollobás and James’ theorems is also presented.
Some invariant biorthogonal sets with an application to coherent states
2014
We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the Hilbert space, and we apply the procedure to coherent states. We conclude the paper considering a simple application of our construction to pseudo-hermitian quantum mechanics.
Integrability via Reversibility
2017
Abstract A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying quasi-periodic motions, and this behavior persists under perturbations within the class. Real-analytic volume preserving systems are found in this class which have positive Lyapunov exponents on an open subset, and the complement filled with invariant tori.
Existence of common zeros for commuting vector fields on 3‐manifolds II. Solving global difficulties
2020
We address the following conjecture about the existence of common zeros for commuting vector fields in dimension three: if $X,Y$ are two $C^1$ commuting vector fields on a $3$-manifold $M$, and $U$ is a relatively compact open such that $X$ does not vanish on the boundary of $U$ and has a non vanishing Poincar\'e-Hopf index in $U$, then $X$ and $Y$ have a common zero inside $U$. We prove this conjecture when $X$ and $Y$ are of class $C^3$ and every periodic orbit of $Y$ along which $X$ and $Y$ are collinear is partially hyperbolic. We also prove the conjecture, still in the $C^3$ setting, assuming that the flow $Y$ leaves invariant a transverse plane field. These results shed new light on t…
Coprime actions and degrees of primitive inducers of invariant characters
2001
Let a finite group A act coprimely on a finite group G and χ ∈ Irr A(G). Isaacs, Lewis and Navarro proved that if G is nilpotent then the degrees of any two A-primitive characters of A-invariant subgroups of G inducing χ coincide. In this note we aim at extending this result by weakening the hypothesis on G.
Boundary quotients and ideals of Toeplitz C∗-algebras of Artin groups
2006
We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G,P), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica spectrum of (G,P). Our original motivation and our main examples are drawn from right-angled Artin groups, but many of our results are valid for more general quasi-lattice ordered groups. We show that the Nica spectrum has a unique minimal closed invariant subset, which we call the boundary spectrum, and we define the boundary quotient to be the crossed product of the corresponding restricted partial action. The main technical tools used are the results of …