Infinite algebras with few subalgebras of powers

Date

Oct 19, 2017

Time

1:15 PM - 2:15 PM

Speaker

Jakub Oprsal

Affiliation

TU Dresden, Institut für Algebra

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. M. Bodirsky

Description

For a finite algebra, there can be up to doubly exponentially many in $n$ subalgebras of the $n$-th power. It is known that if this is not the case, the algebra has few subpowers, i.e., there is a polynomial $p$ such that there are at most $2^{p(n)}$ subalgebras of the $n$-power. All finite algebras having this property have been characterized in 2009 by Berman, Idziak, Markovic, McKenzie, Valeriote, and Willard. In the talk, we will focus on infinite algebras with few subpowers; in particular we require that we have a finite number of subalgebras of powers. These algebras seems to be much rarer than their finite counterparts. We will give a few examples, and describe how the clasification of the finite algebras generalize to the infinite, and in particular to algebras that are obtained by taking polymorphisms of countable structures.

Last modified: Oct 12, 2017, 6:37:27 PM