Reflection-closed varieties of multisorted algebras and minor identities

Date

Jun 9, 2017

Time

1:15 PM - 2:15 PM

Speaker

Dr. Erkko Lehtonen, Prof. Dr. Reinhard Pöschel

Affiliation

TU Dresden, Institut für Algebra

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Dr. E. Lehtonen

Description

Reflections (as introduced by L. Barto, J. Opršal, M. Pinsker) generalize the classical operators of taking subalgebras and homomorphic images. We generalize this notion to multisorted algebras. We ask for a characterization of reflection-closed varieties (RP-varieties) and consider the Galois connection Mod-mId between multisorted algebras and minor identities. Analogously to the classical Birkhoff theorem, it turns out that the Galois closed sets of algebras are just the reflection-closed varieties of multisorted algebras, i.e., Mod mId K = RP K. Similarly, we characterize the minor-equational theories of multisorted algebras, i.e., the closed sets of minor identities. We also discuss how RP-varieties and usual varieties of multisorted algebras are related to each other. This is joint work with Tamás Waldhauser.

Links

• Institut für Algebra: International Seminar

Last modified: Jun 1, 2017, 6:16:41 PM