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The Auslander-Gorenstein property for Z-algebras
We provide a framework for part of the homological theory of Z-algebras and
their generalizations, directed towards analogues of the Auslander-Gorenstein
condition and the associated double Ext spectral sequence that are useful for
enveloping algebras of Lie algebras and related rings. As an application, we
prove the equidimensionality of the characteristic variety of an irreducible
representation of the Z-algebra, and for related representations over quantum
symplectic resolutions. In the special case of Cherednik algebras of type A,
this answers a question raised by the authors.Comment: 31 page
Analyticity in spaces of convergent power series and applications
We study the analytic structure of the space of germs of an analytic function
at the origin of \ww C^{\times m} , namely the space \germ{\mathbf{z}} where
\mathbf{z}=\left(z\_{1},\cdots,z\_{m}\right) , equipped with a convenient
locally convex topology. We are particularly interested in studying the
properties of analytic sets of \germ{\mathbf{z}} as defined by the vanishing
locus of analytic maps. While we notice that \germ{\mathbf{z}} is not Baire we
also prove it enjoys the analytic Baire property: the countable union of proper
analytic sets of \germ{\mathbf{z}} has empty interior. This property underlies
a quite natural notion of a generic property of \germ{\mathbf{z}} , for which
we prove some dynamics-related theorems. We also initiate a program to tackle
the task of characterizing glocal objects in some situations
Z-actions on AH algebras and Z^2-actions on AF algebras
We consider Z-actions (single automorphisms) on a unital simple AH algebra
with real rank zero and slow dimension growth and show that the uniform
outerness implies the Rohlin property under some technical assumptions.
Moreover, two Z-actions with the Rohlin property on such a C^*-algebra are
shown to be cocycle conjugate if they are asymptotically unitarily equivalent.
We also prove that locally approximately inner and uniformly outer Z^2-actions
on a unital simple AF algebra with a unique trace have the Rohlin property and
classify them up to cocycle conjugacy employing the OrderExt group as
classification invariants.Comment: 24 page
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