C∗-algebras Associated Noncommutative Circle and Their K-theory
نویسنده
چکیده
In this article we investigate the universal C∗-algebras associated to certain 1dimensional simplicial flag complexes which describe the noncommutative circle. We denote it by S 1 . We examine the K-theory of this algebra and the subalgebras S nc 1 /Ik, Ik . Where Ik, for each k, is the ideal in S 1 generated by all products of generators hs containing at least k + 1 pairwise different generators. Moreover we prove that such algebra divided by the ideal I2 is commutative.
منابع مشابه
Classification of simple C * - algebras and higher dimensional noncommutative tori
We show that unital simple C-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C-algebras can be classified by their ordered K-theory. We apply this classification result to show that certain simple crossed products are isomorphic if they have the same ordered K-theory. In particular, irrational higher dimensional noncommutative tori of the form C(T)×θ...
متن کاملThe Erwin Schrr Odinger International Institute for Mathematical Physics K{theory of Noncommutative Lattices K-theory of Noncommutative Lattices
Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutati...
متن کاملESI The Erwin Schr
Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutati...
متن کاملK-theory of Noncommutative Lattices
Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of ‘continuous functions’ which turn out to be noncomm...
متن کاملThe Noncommutative Geometry of Graph C-algebras I: the Index Theorem
We investigate conditions on a graph C∗-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth (1,∞)-summable semfinite spectral triple. The local index theorem allows us to compute the pairing with K-theory. This produces invariants in the K-theory of the fixed point algebra, and these ...
متن کامل