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UID:8683@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250320T170000
DTEND;TZID=Europe/Paris:20250320T180000
DTSTAMP:20250518T224806Z
URL:https://www.i2m.univ-amu.fr/evenements/tbao/
SUMMARY:Maxime Sommella (I2M (AMU)): An Introduction to Non-Associative Alg
 ebras & Jordan Algebras
DESCRIPTION:Maxime Sommella: \n\n\n\n\n\nAbstract : Associativity is one of
  the most fundamental properties in mathematics. Almost all natural operat
 ions you can think of are associative : concatenation\, union and intersec
 tion of sets\, composition of functions etc. This property is so natural t
 hat it is often overlooked and we tend to forget that “(2+3)+4” and 
 “2+(3+4)” don’t really have the same meaning.\n\nBut examples of non
 -associative algebras are quite easy to find. Using a process called the C
 ayley-Dickson Construction\, you can enlarge the algebra of real numbers $
 \\mathbb{R}$ to get the following inclusions of $\\mathbb{R}$-algebras : $
 \\mathbb{R} \\subset \\mathbb{C} \\subset \\mathbb{H} \\subset \\mathbb{O}
  \\subset \\mathbb{S} \\subset \\mathbb{T} \\subset …$\, where all the a
 lgebras containing the algebra of the so-called octonions ($\\mathbb{O}$) 
 are no-longer associative (i.e. the multiplication is no longer associativ
 e).\n\nIn 1933\, Pascual Jordan introduced a new class of algebras encompa
 ssing numerous examples of non-associative algebras (but also associative 
 ones) in an attempt to formalize the notion of observables in quantum elec
 trodynamics. Despite the fact that these algebras didn’t find many appli
 cations in physics\, they became of great interest for mathematicians them
 selves.\n\nIn this talk I will try to give you a (hopefully) accessible in
 troduction to the theory of non-associative algebras and Jordan algebras w
 ith the aim of stating the Classification Theorem for Finite-Dimensional J
 ordan Algebras.\n\nPS : And if we have time\, I will try to compute in fro
 nt of you without my notes the very difficult calculations “(2+3)+4” a
 nd “2+(3+4)” (get ready because this is pretty impressive...).\n\n\n\n
 \n\n\n\nLe séminaire des doctorant⋅es de l'I2M et du CPT à Luminy regr
 oupe chaque semaine les doctorant⋅es du site autour d'un exposé plus ou
  moins (in)formel\, dans un cadre convivial. Il est évidemment ouvert aux
  étudiant⋅es de master et aux doctorant⋅es d'autres laboratoires.\n\n
 Pour le moment\, le séminaire a lieu dans la salle 500-504b du TPR2\, au 
 5ème étage.
CATEGORIES:Séminaire,Rencontres doctorant⋅es I2M-CPT
LOCATION:Luminy - salle 500-504b\, Aix-marseille université-faculté des s
 ciences\, campus Luminy\, Marseille\, France
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 aculté des sciences\, campus Luminy\, Marseille\, France;X-APPLE-RADIUS=1
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TZOFFSETTO:+0100
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