The topology of the set of nonsoliton Lie algebras in the moduli space of nilpotent Lie algebras

TL;DR

This paper investigates the structure of nonsoliton nilpotent Lie algebras within the moduli space, revealing that their set is discrete only in dimensions up to 7, which advances understanding of their geometric properties.

Contribution

It characterizes the topological nature of nonsoliton Lie algebras in the moduli space, establishing a dimension threshold for discreteness.

Findings

Nonsoliton Lie algebras form a discrete set in dimensions up to 7.

Beyond dimension 7, the set of nonsoliton Lie algebras is not discrete.

The result links algebraic properties to geometric topology in the moduli space.

Abstract

A Lie algebra is called nonsoliton if it does not admit a soliton inner product. We demonstrate that the subset of nonsoliton Lie algebras in the moduli space of indecomposable n-dimensional N-graded nilpotent Lie algebras is discrete if and only if n <= 7.