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SUMMARY:Lorna Gregory (UEA)
DTSTART:20250318T140000Z
DTEND:20250318T150000Z
DTSTAMP:20260421T154346Z
UID:UEAPS/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/50/">R
 epresentation Type\, Decidability and Pseudofinite-dimensional Modules ove
 r Finite-dimensional Algebras</a>\nby Lorna Gregory (UEA) as part of ANTLR
  seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nThe representation ty
 pe of a finite-dimensional k-algebra is an algebraic measure of how hard i
 t is to classify its finite-dimensional indecomposable modules. Intuitivel
 y\, a finite-dimensional k-algebra is of tame representation type if we ca
 n classify its finite-dimensional modules and wild representation type if 
 its module category contains a copy of the category of finite-dimensional 
 modules of all other finite-dimensional k-algebras. An archetypical (altho
 ugh not finite-dimensional) tame algebra is k[x]. The structure theorem fo
 r finitely generated modules over a PID describes its finite-dimensional m
 odules. Drozd’s famous dichotomy theorem states that all finite-dimensio
 nal algebras are either wild or tame.\n\n\nThe (theory of) a class of modu
 les is said to be decidable if there is an algorithm which given a sentenc
 e in the language of modules (a sentence is a particular kind of statement
  about modules) answers whether it is true in all modules in that class. A
  long-standing conjecture of Mike Prest claims that the (theory of) the cl
 ass of all modules over a finite-dimensional algebra is decidable theory i
 f and only if it is of tame representation type. The reverse direction of 
 this conjecture is often hard to prove even in particular examples. One di
 fficulty is that the conjecture talks about all modules rather than just f
 inite-dimensional ones. In this talk I will present work in progress aroun
 d and in support of a new conjecture\, inspired by Prest’s conjecture\, 
 which claims that the (theory of) the class of finite-dimensional modules 
 over a finite-dimensional algebra is decidable if and only if it is of tam
 e representation type.\n
LOCATION:https://researchseminars.org/talk/UEAPS/50/
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