Related papers: The Cyclic Vector Lemma

Given a closed Riemannian manifold $(M^m,g)$ and a vector field $v$ on $M$, we form the Sasaki metric $g_S$ on $TM$, and restrict it to the image of the cross section map of $M$ into $TM$ defined by $v$, whose pull back to $M$ defines a new…

We obtain Fuchs decomposition theorem for regular singular differential modules over a large class of differential rings. We provide a definition of regularity inspired by differential Galois theory and we deduce the classical equivalence…

We prove that a vector field on an affine $C^\infty$-scheme Spec(A) has a flow if the $C^\infty$-ring A is finitely generated. If the vector field is complete then the flow is the target map of a groupoid internal to the category of…

We prove that an iterative derivation $\delta_F$ on a field $F$ can be extended to an iterative derivation $\delta_A$ on a central simple $F-$algebra $A$ if the characteristic of $F$ does not divide the exponent of $A$ in the Brauer group…

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let $A$ be a regular domain and let $K$ be its field of…

Let $V$ be a complete discrete valuation ring with fraction field $F$ of characteristic zero and with residue field $\mathbb{F}$. We introduce analytic cyclic homology of complete torsion-free bornological algebras over $V$. We prove that…

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…

Let $k$ be a differential field of characteristic zero and the field of constants $C$ of $k$ be an algebraically closed field. Let $E$ be a differential field extension of $k$ having $C$ as its field of constants and that $E=E_m\supseteq…

Let $G$ be a connected reductive $p$-adic group and let $\theta$ be an automorphism of $G$ of order at most two. Suppose $\pi$ is an irreducible smooth representation of $G$ that is taken to its dual by $\theta$. The space $V$ of $\pi$ then…

Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F)]-modules. For these…

The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is given by the source vertical tangent bundle restricted to the identity bisection. Its sections can be identified with the invariant vector…

We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is…

For a finite subgroup $G$ of $SU(2)$ and one of its ground forms $P\in\mathbb{C}[X,Y]$, we show that the space of invariants $\mathbb{C}[X,Y,P^{-1}]^{G}_k$ of degree $k\in2\mathbb{Z}$ is a cyclic module over the algebra of invariants of…

Let $\Phi $ be a Drinfeld $\mathbf{F}\_{q}[T]$-module of rank 2, over a finite field $L=\mathbf{F}\_{q^{n}}$. We will study the cyclic property of the structure $L^{\Phi}.$ We will prove that the latter is cyclic only for trivial extensions…

In this paper we describe the Dieudonn\'e crystal of a finite locally free group scheme with a vector action of a finite field $\mathbb{F}$. These $\mathbb{F}$-vector schemes appear when we consider torsion points of $p$-divisible modules.…

Let $R$ be a regular local ring containing a field $k$ of characteristic $p$ and $M$ be an $\mathscr{F}$-finite module. In this paper, we study the injective dimension of $M$. We prove that $\operatorname{dim}_R(M) -1…

For a totally real field $F$, a finite extension $\mathbf{F}$ of $\mathbf{F}_p$ and a Galois character $\chi: G_F \to \mathbf{F}^{\times}$ unramified away from a finite set of places $\Sigma \supset \{\mathfrak{p} \mid p\}$ consider the…

In this paper, we generalize the definition of the differential Galois group and the Galois correspondence theorem established previously for Picard-Vessiot extensions of real differential fields with real closed field of constants to any…

Let $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ be a Levi decomposable Lie algebra, with Levi factor $\mathfrak{s}$, and radical $\mathfrak{r}$. A module $V$ of $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ is cyclic indecomposable if it is…

Let f be a modular eigenform of even weight k>0 and new at a prime p dividing exactly the level, with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D_FM(f) and an…