In a recent paper,1 K. Asano gave a new proof of the theorem that a domain of integrity has a right quotient ring if and only if every pair of nonzero elements has a common nonzero right multiple. His method of proof is used in the present work to extend the centralizer of a ring over a module to a system of semi-endomorphisms of the module. From this extension, necessary and sufficient conditi...

For each d, we construct CAT(0) cube complexes on which Cremona groups of rank d act by isometries. From these actions deduce new and old group-theoretical dynamical results about groups. In particular, study the behavior irreducible components exceptional loci. This leads to proofs regularization theorems, such as with property FW. We also find constraints degree growth for non-pseudo-regulari...

Write E for the stable discrete series character associated to an irreducible nite-dimensional representation E of a connected real reductive group G. Let M be the centralizer of the split component of a maximal torus T , and denote by M ( ; E) Arthur's extension of jDG M ( )j 12 E( ) to T (R). In this paper we give a simple explicit expression for M ( ; E), when is elliptic in G. We do not ass...

Let p be a prime,G a finite group which has a normal p-subgroup containing its own centralizer inG, and R a commutative local ring with residue class field of characteristic p. In this paper, it is shown that if α is an augmented automorphism of RG which fixes a Sylow p-subgroup P of G, there is ρ ∈ Aut(G) such that xαρ = x for all x ∈ P , and αρ is an inner automorphism of RG.

We assume that the “table head” of the ordinary character table of the sporadic simple Janko group J4 is known. That is, the conjugacy classes and their centralizer orders are known as well as all p-th power maps, for primes p up to the maximal element order in J4, which is 66. For the sake of simplicity, we take the table head of the character table contained in the GAP Character Table Library...

We define a class of transversal slices in spaces which are quasi-Poisson for the action complex semisimple group G. This is multiplicative analogue Whittaker reduction. One example universal centralizer Z G, equipped with usual symplectic structure this way. construct smooth relative compactification Z‾ by taking closure each fiber wonderful By realizing as larger variety, we show that it and ...

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

Let p be a prime. We denote by Sn the symmetric group of degree n, by An the alternating group of degree n and by Fp the field with p elements. An important concept of modular representation theory of a finite group G is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring FqG, where q is a prime...

A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...