Full Duality among Graph Algebras and Flat Graph Algebras
نویسندگان
چکیده
We prove that among finite graph algebras and among finite flat graph algebras, dualizability, full dualizability, strong dualizability and entropicity are all equivalent. Any finite (flat) graph algebra which is not dualizable must be inherently non-κ-dualizable for every infinite cardinal κ. A new, general method for proving strong duality is presented.
منابع مشابه
NILPOTENT 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 کاملOn Spin Models, Triply Regular Association Schemes, and Duality
Motivated by the construction of invariants of links in 3-space, we study spin models on graphs for which all edge weights (considered as matrices) belong to the Bose-Mesner algebra of some association scheme. We show that for series-parallel graphs the computation of the partition function can be performed by using seriesparallel reductions of the graph appropriately coupled with operations in...
متن کاملSTONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES
$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...
متن کاملMultiply generated dynamical systems and the duality of higher rank graph algebras
We define a semidirect product groupoid of a system of partially defined local homeomorphisms T = (T1, . . . , Tr). We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use this construction for higher rank graph algebras in order to give a topological interpretation for the duality in E-theory between C∗(Λ) and C∗(Λop). Introducti...
متن کاملGraphs, groupoids and Cuntz-Krieger algebras
We associate to each locally finite directed graph G two locally compact groupoids G and G(?). The unit space of G is the space of one–sided infinite paths in G, and G(?) is the reduction of G to the space of paths emanating from a distinguished vertex ?. We show that under certain conditions their C∗–algebras are Morita equivalent; the groupoid C∗–algebra C∗(G) is the Cuntz–Krieger algebra of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998