[Todos CMAT] Seminario de Álgebra del IMERL - Bernhard Keller (Université Paris Cité)

[seminarios en cmat.edu.uy]

Seminario de Álgebra del IMERL
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Título: "Singularity categories, Leavitt path algebras and Hochschild homology."

Expositor: Bernhard Keller (Université Paris Cité)

Resumen:
 
The singularity category of a noetherian (non commutative) algebra is the
quotient of its bounded by its perfect derived category. This construction goes
back to Buchweitz (1986) in this setting and, independently, to Orlov (2003) in
a geometric setting. We will recall the description of the singularity category
of a radical-square zero quiver algebra using a graded Leavitt path algebra
following work of Paul Smith, Xiao-Wu Chen, Dong Yang and others. We will then
combine this with a localization theorem for Hochschild homology to obtain a
simple description of the Hochschild homology of these singularity categories
(with their canonical differential graded enhancement) and of the corresponding
Leavitt path algebras. Finally, we will report on recent work of Xiao-Wu Chen
and Zhengfang Wang which yields a generalization from radical-square zero to
arbitrary finite-dimensional algebras (over an algebraically closed field).
This is mainly a survey talk. The original parts are based on joint work with
Umamaheswaran Arunachalam and Yu Wang.
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Viernes 7/10 a las 11:15, Sala de Seminarios del IMERL y 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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