Seminario / Fernández-Alcober
The Ischia Group Theory 2020 Conference (http://www.dipmat2.unisa.it/ischiagrouptheory/)
was planned for 30 March - 4 April 2020. It has now been postponed to 2021.
In the meantime, we are offering a series of online lectures
by leading researchers (https://sites.google.com/unisa.it/e-igt2020/).
TIME: June 4, 2020 17:00 CEST (UTC+2)
COFFEE BREAK: The talk will start at 17:00 CEST.
The conference roomwill open at 16:45 CEST for a coffee break
- Bring Your Own tea/coffeemug - biscuits appreciated -
and join us for some small talk before the event.
SPEAKER: Gustavo A. Fernández-Alcober
(University of the Basque Country UPV/EHU)
TITLE: Elementary equivalence for
partially commutative nilpotent groups and algebras
- The TIME OF THE TALK is 17:00 CEST.
- The Zoom link is NEW.
- You are welcome to share the Zoom link with other interested
parties, but PLEASE DO NOT POST THE LINK PUBLICLY.
- When joining, please MAKE SURE THAT YOUR NICKNAME
IS YOUR NAME ANDSURNAME, or close to it,
so that the organisers can recognise you and let you in
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.