منابع مشابه
Nonstable K-theory for Graph Algebras
We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V (LK(E)). When K is the field C of complex ...
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Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state (cf. Jiang and Su [11]). Let A 6= 0 be a unital C∗-algebra with A ∼= A ⊗ Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, πi(U(A)) ∼= Ki−1(A) for all integer i ≥ 0. Furthermore, A has cancellation for full projections, and satisfies the comparability quest...
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We consider algebraic structure of Quantum Theory and provide its combinatorial representation. It is shown that by lifting to the richer algebra of graphs operator calculus gains simple interpretation as the shadow of natural operations on graphs. This provides insights into the algebraic structure of the theory and sheds light on the combinatorial nature and philosophy hidden behind its forma...
متن کاملOn the K-theory of higher rank graph C*-algebras
Abstract. Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C-algebra, C(Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C(Λ). The Kgroups of C(Λ) for k > 2 can be calculated under certain circumstances and we consider the case k = 3. We prove that for arbitrary k, the torsion-free rank of K0(C∗(Λ)) and K1(C∗(Λ)) ...
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An analysis is given of ∗-representations of rank 2 single vertex graphs. We develop dilation theory for the nonselfadjoint algebras Aθ and Au which are associated with the commutation relation permutation θ of a 2 graph and, more generally, with commutation relations determined by a unitary matrix u in Mm(C)⊗Mn(C). We show that a defect free row contractive representation has a unique minimal ...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2006
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-006-9044-z