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UID:7hbp5fcpc1r0cdq5a6nk4tuu62@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Erkko Lehtonen (Technische Universität Dresden): Graph algebras and graph varieties
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. Graph algebras were introduced by Shallon in 1979. To each direct
ed graph G=(V,E), we associate an algebra A(G) of type (2), whose universe
is the set V∪{∞}, where ∞ is a new element not in V, and where the binary o
peration ("product") is defined as xy = x if (x,y)∈E and xy = ∞ otherwise.
Encoding graphs as algebras in this way, we can view any algebraic properti
es of the graph algebra A(G) as properties of the graph G.\n\nAlthough the
class of graph algebras does not constitute a variety (as it is not closed
under direct products), it makes perfect sense to consider the satisfaction
relation between graphs (that is, graph algebras) and identities in the la
nguage of groupoids. Accordingly, the equational classes of graphs are call
ed graph varieties. Graph varieties have been investigated by several autho
rs. For example, Kiss, Pöschel and Pröhle determined the identities satifie
d by all graphs. Poomsa-ard and his coauthors have characterized the graph
varieties axiomatized by the transitive and the left or right self-distribu
tive identities.\n\nContinuing this line of research, we determined the gra
ph varieties axiomatized by certain groupoid identities that are of general
interest in algebra, such as the medial, (left or right) semimedial, idemp
otent, unipotent, zeropotent, and alternative identities.\n\nThis is joint
work with Chaowat Manyuen (Khon Kaen University).
DTSTAMP:20200707T074802Z
DTSTART;TZID=Europe/Budapest:20180926T100000
DTEND;TZID=Europe/Budapest:20180926T120000
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