Symmetry classes of tensors and semi-direct product of finite abelian groups

In the study of symmetry classes of tensors, finding examples of symmetry classes of tensors that possess an o*-basis is of considerable interest. There are only few classes of groups that have been provided a necessary and sufficient condition for having such a basis. There is no general criterion for any finite group yet. In this note, we provide a necessary and sufficient condition for the existence of o*-basis of symmetry classes of tensors associated with semi-direct product of some finite abelian groups and, consequently, their wreath product.     

Hilbert W*-模上的广义框架

本文研究了Hilbert W*-模上的广义框架.运用了算子理论的方法,得出了Hilbert W*-模上的广义框架的一些结果,与标准离散Hilbert C*-模框架的一些结果是相似的.     

GESFIDE-PROPELLER Approach for Simultaneous R2 and R2* Measurements in the Abdomen

Purpose

To investigate the feasibility of combining GESFIDE with PROPELLER sampling approaches for simultaneous abdominal R2 and R2* mapping.

Materials and Methods

R2 and R2* measurements were performed in 9 healthy volunteers and phantoms using the GESFIDE-PROPELLER and the conventional Cartesian-sampling GESFIDE approaches.

Results

Images acquired with the GESFIDE-PROPELLER sequence effectively mitigated the respiratory motion artifacts, which were clearly evident in the images acquired using the conventional GESFIDE approach. There was no significant difference between GESFIDE-PROPELLER and reference MGRE R2* measurements (p = 0.162) whereas the Cartesian-sampling based GESFIDE methods significantly overestimated R2* values compared to MGRE measurements (p < 0.001).

Conclusion

The GESFIDE-PROPELLER sequence provided high quality images and accurate abdominal R2 and R2* maps while avoiding the motion artifacts common to the conventional Cartesian-sampling GESFIDE approaches.     

On stability of index of Fredholm complexes on the C* -algebra

This article deals with the index of Fredholm complexes of Λ-operators of the Hilbert Λ-modulus on C*-algebra. For this class of operators necessary and sufficient conditions in order to be a Fredholm, are obtained. Based on these results, a notion of Fredholm complex and its index is introduced. For this index, a stability theorem related to various perturbations is proved. In the second part of the article, a completation of a semigroup Fredholm complexes is analysed. It is proved that the group K _G (X, Λ) is the completation of G ? Λ-fibration of the above group on the compact space X.     

Lie *-Nilpotence of Group Rings

Let KG be the group ring of a group G over a field K. Let * be an involution of a group G extended linearly to the group ring KG. Suppose that G is a torsion group without 2-elements and K is a field with characteristic different from 2. We prove that KG is Lie *-nilpotent if and only if KG is Lie nilpotent.     

On the Simplicity of the Lie Algebra of a Leavitt Path Algebra

For a field F and a row-finite directed graph Γ, let L(Γ) be the associated Leavitt path algebra. We find necessary and sufficient conditions for the Lie algebra [L(Γ), L(Γ)] to be simple.     

Some Results on Hypercentral Units in Integral Group Rings

Abstract

In this note we investigate the hypercentral units in integral group rings ?G,where G is not necessarily torsion. One of the main results obtained is the following (Theorem 3.5): if the set of torsion elements of G is a subgroup T of G and if Z ₂(𝒰) is not contained in C _𝒰(T),then T is either an Abelian group of exponent 4 or a Q* group. This extends our earlier result on torsion group rings.     

极分解与广义*-Aluthge变换

首先给出了Hilbert空间上有界线性算子极分解的的若干性质.其次指出广义的*-Aluthge变换与*-Aluthge变换具有许多相似性质;例如,T_(α,β)^((*))=U|T_(α,β)((*))=U|T_(α,β)^((*))|当且仅当T是双正规的,即[|T|,|T*|]=0,其中对任意两个算子A和B,[A,B]=AB-BA.