[Todos CMAT] Seminario de Álgebra del IMERL - John MacQuarrie (Universidade Federal de Minas Gerais)

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Seminario de Álgebra del IMERL
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Título: "Extensions of algebras and preservation of the finitude of the finitistic dimension"

Expositor: John MacQuarrie (Universidade Federal de Minas Gerais)

Resumen:
 
An extension of (unital, associative) algebras is simply an algebra A with
subalgebra B.  I will discuss two projects relating the homological properties
of A and B under certain assumptions on the extension.  In a sequence of
articles,Cibils, Lanzilotta, Marcos e Solotar prove that both the finitude of
the global dimension and of the support of the Hochschild homology are preserved
by what they call "bounded extensions".  In joint work with Kostiantyn Iusenko,
we extend this result to a wider class of extensions that includes certain
infinite dimensional extensions of interest to us (we allow, for instance,
(completed) path algebras with loops and cycles).  We also add to the list the
preservation of the finitude of the finistisic dimension.  These results have
the form "A has a property iff B does".  The second project, joint work with
Fernando dos Reis Naves, considers the question "If A has finite finitistic
dimension, when can we say that B does too?": I'll show that the hypotheses on
the extension can be weakened considerably.
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Viernes 28/10 a las 11:15, A través de Zoom

Contacto: Marco A. Pérez - mperez en fing.edu.uy
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Zoom link for remote participants:

https://salavirtual-
udelar.zoom.us/j/85879414417?pwd=S3RqWHpuUXdGeHhucUNTa251Y1pZdz09   Meeting ID:
858 7941 4417  Passcode:   FGc=6*c en HV
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