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Bunce–Deddens Algebra
In mathematics, a Bunce–Deddens algebra, named after John W. Bunce and James A. Deddens, is a certain type of AT algebra, a direct limit of matrix algebras over the continuous functions on the circle, in which the connecting maps are given by embeddings between families of shift operators with periodic weights. Each inductive system defining a Bunce–Deddens algebra is associated with a supernatural number, which is a complete invariant for these algebras. In the language of operator K-theory, K-theory, the supernatural number correspond to the group of the algebra. Also, Bunce–Deddens algebras can be expressed as the -crossed product of the Cantor set with a certain natural minimal action known as an ''odometer action''. They also admit a unique tracial state. Together with the fact that they are AT, this implies they have real rank (C*-algebras)#Real rank zero, real rank zero. In a broader context of the classification program for simple (abstract algebra), simple separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
