Cyclic metric Lie groups

TL;DR

This paper studies cyclic metric Lie groups, focusing on their classification in low dimensions, and explores their structure in semisimple and solvable cases, extending previous classifications to more general cases.

Contribution

It extends classifications of cyclic metric Lie groups to the general case beyond unimodular groups in low dimensions.

Findings

Classification of unimodular cyclic metric Lie groups up to dimension five

Analysis of semisimple and solvable cyclic metric Lie groups

Extension of existing classifications to more general cases

Abstract

Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and solvable cases are studied. We extend to the general case, Kowalski-Tricerri's and Bieszk's classifications of connected and simply-connected unimodular cyclic metric Lie groups for dimensions less than or equal to five.