CUNTZ-PIMSNER ALGEBRAS OF GROUP ACTIONS

By Volodymyr V. Nekrashevych. 2004

179 citations recorded by the source corpus.

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Citations in the corpus

The tight groupoid of an inverse semigroup (2014, methodology): “To mention an example of interest to us, in [6] and [7] a unified treatment was given to a certain class of C*-algebras studied by Katsura in [9], alongside Nekrashevych’s C*algebras introduced and discussed in [12], [13] and [14].”
Simple groups separated by finiteness properties (2017, background): “gn ∈G. Note that Vd(G) really is a subgroup of AAut(Td), since self-similarity ensures that it is closed under multiplication. Nekrashevych groups were ﬁrst introduced in this degree of generality in [Nek04]. The ﬁrst such group considered was the Rover group [Ro¨v99], which is V 2(Grig) for Grig th”
Branch rings, thinned rings, tree enveloping rings (2004, background): “, in the category of C∗-algebras, then the deﬁnition becomes much more intricate due to the absence of free objects in that category. The best approach is probably that of a C∗-bimodule considered in [34]. An important feature is missing from the algebras of §3.1.1, namely the existence of ﬁnite-dim”
Etale groupoids arising from products of shifts of finite type (2015, background): “They are regarded as generalizations of the Higman-Thompson groups (see [29, 28]).”
Topological full groups of one-sided shifts of finite type (2012, background): “Nekrashevych [34] observed that [[G]] is naturally isomorphic to the Higman-Thompson group Vn,1 when (X,σ) is the full shift over n symbols (see Remark 6.”
Zappa-Sz\'ep products of semigroups and their C*-algebras (2013, background): “A seemingly unrelated class of C-algebras has recently been discovered by Nekrashevych [22, 24], namely those associated with self-similar group actions.”
Simple groups of dynamical origin (2015, background): “See more for the groups of this type in [23, 24].”
On C*-algebras associated to right LCM semigroups (2014, background): “The CuntzPimsner algebra O(G,X) of a self-similar group has been studied in [23, 25], and the Toeplitz algebra T (G,X) has been studied in [13].”
Partial actions: a survey (2011, unknown): “Nekrashevich in [77].”
Finite Factor Representations of Higman-Thompson groups (2012, background): “To finish our discussion, we notice that the full group of the one-sided Bernoulli shift over the alphabet with n letters is isomorphic to Gn;1 [12].”
Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras (2014, methodology): “Inspired by Nekrashevych’s paper [24], we will now give a description of OG,E as a CuntzPimsner algebra [29].”