Types of polynomial completeness for expanded groups

Sprache des Vortragstitels:

Deutsch

Original Tagungtitel:

71st Workshop on General Algebra (AAA71) together with 21st Conference for Young Algebraists (CYA21)

Sprache des Tagungstitel:

Deutsch

Original Kurzfassung:

From results of Maurer, Rhodes, and Fr\"ohlich, we know
that every function on a finite simple non-abelian group
is a polynomial function; these groups are called
\emph{polynomially complete}. Later, it was studied when
every congruence preserving function on an algebra is
a polynomial function; such algebras were called \emph{affine complete}.
In 2001, P.\ Idziak and K.\ S\l omczy\'nska introduced the concept
of \emph{polynomial richness}.
In general, it seems hard to characterize when a single algebra
is affine complete or polynomially rich.
Characterizations of affine complete algebras have been given for
abelian groups (N\"obauer, Kaarli) and for finite
algebras with a Mal'cev polynomial that have a distributive
congruence lattice (Hagemann, Herrmann, Kaarli).
It is not known if there is an algorithm that decides
whether a given finite algebra (of finite type, with
given operation tables for all operations) is affine complete.
We will investigate finite modular lattices that satisfy a condition
that is more general than distributivity. Based on work
by Idziak and S\l omczy{\'n}ska, we can characterize affine complete
and polynomially rich
algebras among those finite algebras that have a group operation
among their binary polynomial functions, and whose congruence
lattice satisfies this condition on the congruence lattice.
This is joint work with Neboj\v{s}a Mudrinski (Novi Sad).

Sprache der Kurzfassung:

Englisch

Vortragstyp:

Vortrag auf einer Tagung (nicht referiert)

Vortragsdatum:

11.02.2006

Vortragsort:

Polen

Details zum Vortragsort:

Mathematical Research and Conference Center of the Polish Academy of Sciences Bedlewo