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SUMMARY:Presenting isomorphic finitely presented modules by equivalent mat
rices: a constructive approach
DTSTART;VALUE=DATE-TIME:20210429T083000Z
DTEND;VALUE=DATE-TIME:20210429T093000Z
DTSTAMP;VALUE=DATE-TIME:20210508T041700Z
UID:indico-event-6643@indico.math.cnrs.fr
DESCRIPTION:Speakers: Cyrille Chenavier (UniversitĂ© de Limoges)\nÂ A mult
idimensional linear system can be studied by means of its\nassociated modu
le\, presented by the unknown functions of this system\nsubject to the equ
ations. Testing whether two linear systems/modules are\nisomorphic (the so
-called equivalence problem) is an important issue. In\nthis presentation\
, I will first recall from a previous work of\nThomas Cluzeau and Alban Qu
adrat an explicit characterisation for a\nmodule morphism to be an isomorp
hism. Then\, I will recall how they\nobtained a constructive version of a
result due to Fitting\, which shows\nhow to enlarge matrices presenting is
omorphic modules by blocks of zeros\nand identities to get equivalent matr
ices. Finally\, I will present an\ninductive procedure for reducing the si
ze of these two equivalent\nmatrices. It turns out that this procedure ena
bles us to recover a result\ndue to Warfield.\nhttps://indico.math.cnrs.fr
/event/6643/
LOCATION:https://bbb.unilim.fr/b/vac-m6r-7dv
URL:https://indico.math.cnrs.fr/event/6643/
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