Banach algebras associated to locally compact groups

设G是一个群，即G是一个具有结合运算的集合，使得每个元素都有一个逆。例如，G可以被认为是一组数字，正的或负的，加上，或一组正交变换，即一个线性变换后的平移（仿射群）。我将考虑G配备一个拓扑，使得乘法和逆是连续的。进一步假设拓扑是局部紧的，即G的单位元的邻域系存在由紧集构成的基。我在今后几年的研究工作主要包括：（a）研究G（例如群代数、测度代数和Fourier Stieltjes代数B（G））：B）研究由G的左正则表示生成的von Neumann代数VN（G）中相应的非交换函数空间的对偶Banach代数;（c）B（G）中函数的不动点集或B（G）中幂有界元的VN（G）中的（非结合）Jordan结构.我还将研究巴拿赫代数是predicted冯诺依曼代数，其中将包括predicted霍夫冯诺依曼代数，特别是量子群代数。更具体地说，我将继续研究G的一些重要几何性质，例如：

Let G be a group, i.e. G is a set with an associative operation such that each element has an inverse. For example, G may be taken to be the set of numbers, positive or negative, with addition, or the set of orthogonal transformations i.e. a linear transformation followed by translation (the affine group). I will consider G equipped with a topology such that multiplication and inversion are continues. I will further assume that the topology is locally compact, that is there is basis for the neighborhood system for the identity of G consisting of compact set. My research in the next few years will consist of : (a) the study of geometric, algebraic and topological properties on Banach algebras associated for a G (e.g. group algebra, measure algebra and the Fourier Stieltjes algebra B(G); b) the study of dual Banach algebras of the corresponding non-commutative function space in the von Neumann algebra VN(G) generated by the left regular representation of G; (c) the (non-associative) Jordan structure in VN(G) for the fixed point set of a function in B(G) or power bounded elements in B(G). I will also study Banach algebras which are preduals of von Neumann algebras which will include preduals of Hopf von Neumann algebras, in particular quantum group algebras. More specifically, I will continue to study some important geometric properties of G such as: