Tuesday, May 17, 15:15
Sonia Trepode (Mar del Plata), Characterisations of trivial extension
In this talk we consider the trivial extension of basic connected finite
dimensional algebras where,
by trivial extension, we always mean the trivial extension by the minimal
In general, deciding whether a given algebra is a trivial extension or not
is not an easy
task. In this talk we answer this question by giving, in terms of its quiver
and relations, a
complete characterisation of the trivial extension of a finite dimensional
algebra over a
field. Our theorem provides an algorithm to decide when a finite dimensional
algebra is a
trivial extension or not.
Fernández and Platzeck introduced some cutting sets, that we call admissible
order to study isomorphic trivial extensions in particular cases. Using
and the tools of split by nilpotent extensions, we are able to prove this
result in general.
We characterise the algebras having isomorphic trivial extensions in terms
cuts. Fernández and Platzeck also gave a diagrammatic interpretation of
theorem for isomorphic trivial extensions under some assumptions. Following
ideas, and using the tools of split by nilpotent extensions, we are able to
independent proof of Wakamatsu's result for finite dimensional algebras.
Joint work with Fernández, Elsa; Schroll, Sibylle; Treffinger,
Hipólito and Valdivieso, Yadira.