Sophus Lie: a visionary mathematician. (Sophus Lie: un matemático visionario.)
Isogroups and isosubgroups.
The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of . We study the isotopic liftings of groups and subgroups and we also deal with the differences between an isosubgroup and a subgroup of an isogroup. Finally, some links between this isotheory and the standard groups theory, referred to representation and equivalence relations among groups are shown.
Isorings and related isostructures
The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of Santillis isotheory. We study the isotopic liftings of rings, subrings and ideals, and we also introduce the concept of quotient isoring. By using the isoproduct model, necessary conditions assuring the existence of such isostructures are given. Such conditions are based on the inner laws which originate the associated elements of isotopy. These elements will allow to extend, from a different...
Complex nilpotent Lie algebras of dimension 7 which are not derived from others.
Graphs associated with nilpotent Lie algebras of maximal rank.
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph...
Sophus M. Lie.
Directed pseudo-graphs and Lie algebras over finite fields
The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It is rooted in the representation of each Lie algebra by a certain pseudo-graph. As partial results, it is deduced that there exist, up to isomorphism, four, six, fourteen and thirty-four -, -, -, and -dimensional algebras of the studied family, respectively, over the field . Over , eight and twenty-two - and -dimensional Lie algebras, respectively, are also found. Finally,...
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