Vou apresentar uma classificação das álgebras de Lie nilpotentes de dimensão 6. Esta classificação é válida para todos os corpos incluindo os corpos que não são algebricamente fechados e corpos com característica 2. Na classificação usa-se a teoria das formas quadráticas. Este trabalho foi feito...

The set of idempotents of an arbitrary semigroup has the structure of a so called biordered set (or regular biordered set in the case of von Neumann regular semigroups). These structures were studied in detail in work of Nambooripad (1979) and Easdown (1985). There is a notion of a free...

Uma pseudovariedade diz-se decidível se existe um algoritmo que decida se um dado semigrupo pertence à pseudovariedade. O supremo VvW de duas pseudovariedades V e W é a menor pseudovariedade contendo ambas V e W. Um resultado bem conhecido de D. Albert, R. Baldinger e J. Rhodes estabelece que o...

Free profinite semigroups over pseudovarieties of finite semigroups proved to be crucial for the development of Finite Semigroup Theory since the mid 1980's. However, little is known about their structure when the pseudovariety is "large", like when it consists of all finite semigroups. For this...

Over the last decades, several questions related to the synchronization of automata have been studied. Among the ones that remain open, Černý's Conjecture seems to be the most relevant one. In 2008, at the School on Algebraic Theory of Automata in Lisbon, Mikhail V. Volkov suggested several...

An automatic presentation is a description of a relational structures using regular languages. Informally, an automatic presentation consists of a regular language of abstract representatives for the elements of the structure, such that each relation (of arity $n$, say) can be recognized by a...

FAdo is an ongoing project which aims to provide a set of tools for symbolic manipulation of formal languages. To allow high-level programming with complex data structures, easy prototyping of algorithms, and portability (to use in computer grid systems for example), are its main features. Our...

No contexto do problema geral do estudo da mansidão (completa) do produto semidirecto de pseudovariedades, este trabalho analisa o caso em que o segundo factor é ordem computável.
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Um semigrupo $S$ chama-se ji (join irreducible) se $S\in V\vee W$ implica $S\in V$ ou $S\in W$. Nesta palestra damos um "survey" de vários resultados do livro de q-theory sobre semigrupos ji feito em colaboração com Rhodes.

An effective characterization of piecewise testable languages was given by Simon who proved that a language L is piecewise testable if and only if its syntactic monoid is J-trivial. Nowadays there exist several proofs of this result based on various methods from algebraic theory of regular...