Schlichenmaier, Martin
Published in
Forum Mathematicum

By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields infinitesimal and formal rigidity or these algebras. The first (and up to now only) proof of this important result was given 1989 by Fialowski in an unpubli...

Laures, Gerd McClure, James E.
Published in
Forum Mathematicum

We give a simple sufficient condition for Quinn's “bordism-type spectra” to be weakly equivalent to strictly associative ring spectra. We also show that Poincaré bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's functor from bordism-type theories ...

Bois, Jean-Marie Farnsteiner, Rolf Shu, Bin
Published in
Forum Mathematicum

Let (𝔤,[p])$(\mathfrak {g},[p])$ be a finite-dimensional restricted Lie algebra, defined over an algebraically closed field k of characteristic p > 0. The scheme of tori of maximal dimension of 𝔤 gives rise to a finite group S(𝔤) that coincides with the Weyl group of 𝔤 in case 𝔤 is a Lie algebra of classical type. In this paper, we compute the grou...

Knarr, Norbert Stroppel, Markus
Published in
Forum Mathematicum

We consider polar unitals in projective planes over composition algebras. We prove that the little projective group of such a unital is contained in the centralizer of the polarity defining the unital. This yields information about the full automorphism group of the unital; it is contained in the automorphism group of the normal subgroup generated ...

Chen, Zhen-Qing Kim, Kyeong-Hun
Published in
Forum Mathematicum

In this paper we present an Lp-theory for a class of stochastic partial differential equations (SPDEs in abbreviation) driven by Lévy processes. The SPDEs under consideration can have random coefficients that depend both on the time and space variable. Existence and uniqueness of solutions in various Sobolev spaces are obtained. These Sobolev space...

Deng, Shaoqiang Xu, Ming
Published in
Forum Mathematicum

In this paper, we study Clifford–Wolf translations of Finsler spaces. We give a characterization of those Clifford–Wolf translations generated by Killing vector fields. In particular, we show that there is a natural interrelation between the local one-parameter groups of Clifford–Wolf translations and the Killing vector fields of constant length. I...

Lu, Guozhen Ruan, Zhuoping
Published in
Forum Mathematicum

In this paper, we use the discrete Littlewood–Paley–Stein analysis to get the duality result of the weighted product Hardy space for arbitrary number of parameters under a rather weak condition on the product weight w∈A ∞ (ℝ n 1 ×⋯×ℝ n k )$w \in A_\infty ( {\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k})$ . We will show that for any k ...

Stoimenow, Alexander
Published in
Forum Mathematicum

The concept of adequacy of a link was introduced to determine its crossing number. We give crossing number estimates for the (much larger) class of semiadequate links, in particular improving the previously known estimates for positive links. We also give examples showing that semiadequacy may not be attained in minimal crossing number diagrams. Ou...

Guil Asensio, Pedro A. Izurdiaga, Manuel C. Torrecillas, Blas
Published in
Forum Mathematicum

We develop a technique to construct finitely injective modules which are non-trivial, in the sense that they are not direct sums of injective modules. As a consequence, we prove that a ring R is left noetherian if and only if each finitely injective left R-module is trivial, thus answering an open question posed by Salce.

Choo, Zacky Mannan, Wajid Sánchez-García, Rubén J. Snaith, Victor P.
Published in
Forum Mathematicum

We present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on H2n+1(GL(ℂ)). For a cyclotomic field F we define a canonical set of elements in K3(F) and present a novel approach (based on a free differential calculus) to constructing them. Indeed, we are able to explicitly construct their imag...