Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

We study finite dimensional almost- and quasi-effective prolongations of nilpotent ({mathbb {Z}})-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and algebraicity and are appropriate to obtain Levi–Malčev and Levi–Chevalley decompositions and precisions on the heigth and other properties of the prolongations in a very natural way. In a last section we consider the semisimple case and discuss some examples in which the structural algebras are central extensions of orthogonal Lie algebras and their degree ((-,1)) components arise from spin representations.

We derive the existence of p-adic Hurwitz–Lerch L-function by means of a method provided by Washington. This function is a generalization of the one-variable p-adic L-function of Kubota and Leopoldt, and two-variable p-adic L-function of Fox. We also deduce divisibility properties of generalized Apostol–Bernoulli polynomials, in particular establish Kummer-type congruences for them.

Inspired by the work of Lu and Tian (Duke Math J 125(2):351–387, 2004), in this paper we address the problem of studying those Kähler manifolds satisfying the (Delta)-property, i.e. such that on a neighborhood of each of its points the kth power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k (see below for its definition). We prove two results: (1) if a Kähler manifold satisfies the (Delta)-property then its curvature tensor is parallel; (2) if an Hermitian symmetric space of classical type satisfies the (Delta)-property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a Kähler manifold satisfies the (Delta)-property then it is a complex space form.

In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff orthogonality, we get an analogue of the Gauss map. Then we can define concepts of principal, Gaussian, and mean curvatures in terms of the eigenvalues of the differential of this map. Considering planar sections containing the normal field, we also define normal curvatures at each point of the surface, and with respect to each tangent direction. We investigate the relations between these curvature types. Further on we prove that, under an additional hypothesis, a compact, connected surface without boundary whose Minkowski Gaussian curvature is constant must be a Minkowski sphere. Since existing literature on the subject of our paper is widely scattered, in the introductory part also a survey of related results is given.

We show that certain Fano eightfolds (obtained as hyperplane sections of an orthogonal Grassmannian, and studied by Ito–Miura–Okawa–Ueda and by Fatighenti–Mongardi) have a multiplicative Chow–Künneth decomposition. As a corollary, the Chow ring of these eightfolds behaves like that of K3 surfaces.

In this paper, we sketch some constructions providing a link between complex-analytic geometry and nonstandard algebraic geometry via a categorical point of view. The analytic category is seen as a completed fiber of a family of nonstandard algebraic geometries by applying a standard part functor. We indicate how various notions of analytic objects fit into this context (as for example banachanalytic spaces, Kähler spaces etc.)

Let p be an odd prime number. We construct explicit uniformizers for the totally ramified extension ({mathbb {Q}}_p(zeta _{p^2},root p of {p})) of the field of p-adic numbers ({mathbb {Q}}_p), where (zeta _{p^2}) is a primitive (p^2)-th root of unity.

For an arbitrary real connected Lie group G we define (mathrm {p}(G)) as the maximal integer p such that (mathbb {Z}^p) is isomorphic to a discrete subgroup of G and (mathrm {q}(G)) is the maximal integer q such that (mathbb {R}^q) is isomorphic to a closed subgroup of G. The aim of this paper is to investigate properties of these two invariants. We will show that if G is a noncompact connected Lie group, then (1le mathrm {q}(G)le mathrm {p}(G)le dim (G/K)) where K is a maximal compact subgroup of G. In the cases when G is an exponential Lie group or G is a connected nilpotent Lie group, we give explicit relationships between these two invariants and a well known Lie algebra invariant (mathcal M(mathfrak {g})), i.e. the maximum among the dimensions of abelian subalgebras of the Lie algebra (mathfrak {g}:=mathrm {Lie}(G)).

A list of possible holonomy groups with indecomposable holonomy representation contained in the exceptional, non-compact Lie group ({mathrm {G}}_2^{*}) was provided by Fino and Kath. The classification is due to the corresponding holonomy algebras and divided into Type I, II and III, depending on the dimension of the socle being 1, 2 or 3, respectively. It was also shown by Fino and Kath that all algebras of Type I, and by the author that all of Type III are indeed realizable as holonomy algebras by metrics with signature (4, 3). This article proves that this is also true for all Type II algebras. Thus, there exists a realization by a metric for all indecomposable holonomy groups contained in ({mathrm {G}}_2^{*}).

Completely replicable functions play an important role in number theory and finite group theory, in particular the Monstrous Moonshine. In this paper, we give a characterization of completely replicable functions by certain symmetries.