Algebra seminar - Jordan Haden
| Dates: | 28 January 2025 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Jordan Haden |
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Title: 3-Preprojective Algebras of Type D
Abstract: Over an algebraically closed field, Gabriel’s theorem states that the path algebra kQ of a connected quiver is representation-finite if and only if the underlying graph of Q is an ADE Dynkin diagram. Equivalently, kQ is representation-finite precisely when the preprojective algebra of Q is finite-dimensional.
d-Representation-finite (d-RF) algebras, introduced by Iyama and Oppermann, are a generalisation of representation-finite path algebras. Attached to each d-RF algebra is a (d+1)-preprojective algebra. Grant showed that a d-RF algebra is fractional Calabi-Yau precisely when the Nakayama automorphism of its (d+1)-preprojective algebra has finite order.
In this talk, we present a family of algebras which arise from the well-studied 3-preprojective algebras of type A by “taking orbifolds”. We show that a subset of these are themselves 3-preprojective algebras (of type D). Thus we provide new examples of 2-RF algebras, which we show are also fractional Calabi-Yau.
Speaker
Jordan Haden
Organisation: University of East Anglia
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
