A computational procedure on higher-dimensional nilsolitons

Abstract

In this paper, we develop algorithmic approach to classify nilsoliton metrics on dimension 8. This approach includes finding eigenvalue type of the nilsoliton derivation, the nullity type, the index of the algebra. It can be considered as a continuation of our papers in Abstract and Applied analysis, volume 2013, 1 to 7, (2013), with article ID 871930, and in Journal of Symbolic Computation 50 (2013), 350 - 373. In our previous work, we classified only ordered type, nilsoliton metric Lie algebras ie, the algebras with the derivation type (1 < 2 < 3 ... < n) in dimension 8 and 9. Here, we consider more general case. We consider such metrics with simple derivations on an indecomposable nilpotent Lie algebra. In one of our previous study, we have already classified nilsoliton metric Lie algebras with nonsingular Gram matrix in dimension 8 in Journal of Symbolic Computation, vol: 50, 350 - 373, 2013. Here, we focus on the metrics with singular Gram matrix. We also develop faster algorithm in classifying such metrics.