arXiv subjects

Carlos Rafael Payares Guevara

Publications and source records attributed to Carlos Rafael Payares Guevara.

3 recordsLinked to original sources

arXiv2019

Properties of mean dimension and metric mean dimension coming from the topological entropy

In the late 1990's, M. Gromov introduced the notion of mean dimension for a continuous map, which is, as well as the topological entropy, an invariant under topological conjugacy. The concept of metric mean dimension for a dynamical system was introduced by Lindenstrauss and Weiss in 2000. In this paper we will verify which properties coming from the topological entropy map are valid for both mean dimension and metric mean dimension. In particular, we will prove that the metric mean dimension map is not continuous anywhere on the set consisting of continuous maps on both the Cantor set, the interval or the circle. Finally we prove that the metric mean dimension on the set consisting of continuous map on the interval and on the circle is not lower semi-continuous.

math.DS↗

arXiv2019

On simple Lie 2-algebra of toral rank 3

Simple Lie algebras of finite dimension over an algebraically closed field of characteristic 0 or $p> 3$ were recently classified. However, the problem over an algebraically closed field of characteristics 2 or 3 there exist only partial results. The first result on the problem of classification of simple Lie algebra of finite dimension over an algebraically closed field of characteristic 2 is that these algebras have absolute toral rank greater than or equal to 2. In this paper we show that there are not simple Lie 2-algebras with toral rank 3 over an algebraically closed field of characteristic 2 and dimension less or equal to 16.

math.RA↗

arXiv2019

Classical simple Lie 2-algebras of toral rank 3 and a contragredient Lie 2-algebra of toral rank 4

In this paper we show there are no classical type simple Lie 2-algebras with toral rank odd and we also show that the simple contragredient Lie 2-algebra $G(F_{4, a})$ of dimension 34 has toral rank 4, and we give the Cartan decomposition of $G(F_{4, a})$.

math.RA↗