Atomic Representations of Rank 2 Graph Algebras
نویسندگان
چکیده
We provide a detailed analysis of atomic ∗-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic representations. The building blocks are described as the minimal ∗-dilations of defect free representations modelled on finite groups of rank 2.
منابع مشابه
Representations of higher rank graph algebras
Let F+θ be a k-graph on a single vertex. We show that every irreducible atomic ∗-representation is the minimal ∗-dilation of a group construction representation. It follows that every atomic representation decomposes as a direct sum or integral of such representations. We characterize periodicity of F+θ and identify a symmetry subgroup Hθ of Z. If this has rank s, then C(Fθ ) ∼= C(T) ⊗ A for so...
متن کاملNILPOTENT GRAPHS OF MATRIX ALGEBRAS
Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...
متن کاملGames in algebraic logic: axiomatisations and beyond
Outline 1. Algebras of relations: a quick introduction to relation algebras, representable relation algebras 2. Case study: atomic and finite relation algebras • atom structures; representations of finite relation algebras • two examples: McKenzie’s algebra; the so-called ‘anti-Monk algebra’ 3. Games to characterise representability: the games, axioms from games, examples 4. Infinite relation a...
متن کاملDilation Theory for Rank 2 Graph Algebras
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 ...
متن کامل2 8 A pr 2 00 5 COMPACT OPERATORS AND NEST REPRESENTATIONS OF LIMIT ALGEBRAS ELIAS
In this paper we study the nest representations ρ : A −→ Alg N of a strongly maximal TAF algebra A, whose ranges contain non-zero compact operators. We introduce a particular class of such representations, the essential nest representations , and we show that their kernels coincide with the completely meet irreducible ideals. From this we deduce that there exist enough contractive nest represen...
متن کامل