Norddeutsches Gruppentheorie-Kolloquium 2020
Das Norddeutsche Gruppentheorie-Kolloquium 2020 sollte am 17. und 18. Juli 2020 an der Heinrich-Heine-Universität Düsseldorf stattfinden. Aufgrund der anhaltend unsicheren Lage, die sich aus der Coronavirus-Pandemie ergibt, wird das Kolloquium auf unbestimmte Zeit verschoben.
Am Freitag, dem 17. Juli, fand ersatzweise bereits ein Online-Vortrag statt.
Online-Talk (via Cisco Webex) on Friday, 17th July 2020, from 4pm to 5pm (CEST)
Speaker: Gustavo Fernández-Alcober (University of the Basque Country)
Title: Elementary equivalence for partially commutative nilpotent groups and algebras
Abstract: For a fixed algebraic structure (groups, rings, algebras, Lie algebras, ...), two instances of that structure are said to be elementary equivalent if they satisfy the same first-order sentences in the language corresponding to the structure. This way of identifying algebraic objects is weaker than isomorphism, in the sense that isomorphic objects are elementary equivalent, but not necessarily vice versa. On the other hand, Philip Hall introduced the concept of nilpotent R-group, where R is binomial domain, i.e. an integral domain containing the binomial coefficients of its elements.
In this talk we will give an exposition of a joint work with Montserrat Casals, Ilya Kazachkov, and Vladimir Remeslennikov, where we determine all groups/algebras that are elementary equivalent to a partially commutative nilpotent R-group/R-algebra. This is done by building a more general class of well-structured groups/algebras, for which we solve the problem of elementary equivalence.
Eine Auflistung früherer NDGK-Treffen findet sich in Max Horns Übersicht .