C~*代数中的上代数结构(Ⅰ)

30年代由VonNeumann建立的算子代数,经40年代Gelfand等人对抽象C一代数结构的研究,以及60～70年代的VonNeumann代数的因子构造的研究,已经发展得很丰满,并且广泛应用到量子力学的研究中去。线性代数理论方面的另一条线是40年代对Hopf代数的研究,发展成代数—上代数—双代数—Hopf代数的纯代数结构的探索。本文试图寻找两个方向的结合部,即寻找C—代数的上结构和上代数的拓扑结构。本文给出了形式上乘映射,半同态和C双代数的结构,并且证明了任何C—代数都可赋予上结构成为C—双代数。

THE COALGEBRA STRUCTURE IN C*-ALGEBRA(1)

The operator algebra founded by vonNeumann in the 1930's has already grown up to the full and has been extensively applied into the researches in quantum mechanics after the studies of the structures of abstract C* algebra by Gelfand , et al. in the 1940's and those of the factor structures of vonNeumann algebra during the period of the 1960's and 1970's.The other line of the theory of linear algebra is the research on Hopf algebra in the 1940's and this has been developed into the exploration of the stuctures of pure algebras including algebra, coalgebra, bialgebra and Hopf algebra in turn.This Paper attempts to seek some combining Part between C* algebra and Hopf algebra, i.e. to seek the co-structure of C* algebra and the topologic structure of coalgebra. This article offers the formal Co multiplicative map, semi homomorphism and the structure of C* bialgebra and proves that anyC*-algebra can become a C* bialgebra with C* algebra added by co structure.