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Shafarevich Seminar
November 12, 2019 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)
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Minimal models for monomial algebras
P. Tamaroff |
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Abstract:
In 1985, David Anick defined a
combinatorial notion chains which can be used to compute various
homological invariants of an associative algebra from a presentation
of such an algebra by generators and relations that leads to a good
rewriting system. In particular, for algebras with monomial
relations, his construction produces those invariants directly.
In this talk, I will explain how to compute a rich algebraic
structure on Anick chains leading to the explicit formula for a
minimal quasi-free model for any monomial algebra. This computation
relies on algebraic discrete Morse theory and on homotopy transfer
formulas; those are formulas perfectly suited for homological
computations where underlying chain complexes are of combinatorial
nature. Prior knowledge of these techniques is not required: they
will be explained along the way. Additionally, we explain how can
extends the methods used for monomial algebras to algebras with a
good rewriting system in the form of a conjecture and some
examples.
Language: English
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