The outer automorphism group of normalizers of maximal tori in connected compact Lie groups.
[For the entire collection see Zbl 0742.00067.]The Penrose transform is always based on a diagram of homogeneous spaces. Here the case corresponding to the orthogonal group is studied by means of Clifford analysis [see F. Brackx, R. Delanghe and F. Sommen: Clifford analysis (1982; Zbl 0529.30001)], and is presented a simple approach using the Dolbeault realization of the corresponding cohomology groups and a simple calculus with differential forms (the Cauchy integral formula for solutions of...
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.
We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ∖G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
Let = u: u unitary and u-1 compact stand for the unitary Fredholm group. We prove the following convexity result. Denote by the rectifiable distance induced by the Finsler metric given by the operator norm in . If and the geodesic β joining u₀ and u₁ in satisfy , then the map is convex for s ∈ [0,1]. In particular, the convexity radius of the geodesic balls in is π/4. The same convexity property holds in the p-Schatten unitary groups = u: u unitary and u-1 in the p-Schatten class...