The following information was submitted:
Transactions: INTERNATIONAL JOURNAL of APPLIED MATHEMATICS AND INFORMATICS
Transactions ID Number: 20-842
Full Name: Juan Núñez Valdés
Position: Associate Professor
Age: ON
Sex: Male
Address: Dpto de Geometría y Topología. Facultad de Matemáticas. Universidad de Sevilla. Apartado 1160. Sevilla-41080
Country: SPAIN
Tel: 954 557962
Tel prefix: 00 34
Fax: 00 34 954 557070
E-mail address: jnvaldes@us.es
Other E-mails:
Title of the Paper: Classifying filiform Lie algebras in low dimensions over finite fields
Authors as they appear in the Paper: Óscar J. Falcón, Juan Núñez, Ana M. Pacheco, M. Trinidad Villar
Email addresses of all the authors: oscfalgan@yahoo.es, jnvaldes@us.es, ampm@us.es, villar@us.es
Number of paper pages: 9
Abstract: At present, the study of Lie algebras in general and filiform ones in particular is very extended due to their many applications in several branches of Physics or Engineering, for instance. However, the classification of all of the types of Lie algebras, except simple and semi-simple ones, is still an unsolved problem. At this respect, the main goal of this paper is to use some objects of Graph Theory as a tool to classify low-dimensional filiform Lie algebras over finite fields, extending some results already obtained by some of the authors in previous papers. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we find out that there exist, up to isomorphism, six $6$-dimensional filiform Lie algebras over $\mathbb{Z}/p\mathbb{Z}$, for $p=2,3,5$.
Keywords: Bipartite graph; Adjacency matrix; Classification; Filiform Lie algebra; Finite fields; Applications to Physics.
EXTENSION of the file: .pdf
Special (Invited) Session: Low-dimensional filiform Lie Algebras over finite fields
Organizer of the Session: 510-130
How Did you learn about congress: Eugenio Fedriani (efedmar@upo.es), Ángel F. Tenorio (aftenorio@upo.es)
IP ADDRESS: 150.214.148.111
