What question did this study set out to answer?

To explore the structure of 7-dimensional contact nilpotent Lie algebras through explicit calculations and double extensions.

March 29, 2026Open Access

Low Dimensional Contact Lie Algebras

Key Points

To explore the structure of 7-dimensional contact nilpotent Lie algebras through explicit calculations and double extensions.
Calculating the structure of 7-dimensional contact nilpotent Lie algebras.
Describing the relationship between 7-dimensional and 5-dimensional contact nilpotent Lie algebras.
Investigating the representation of (2n+1)-dimensional contact filiform Lie algebras.
Established a framework for representing 7-dimensional contact nilpotent Lie algebras as double extensions.
Illustrated explicit examples of (2n+1)-dimensional contact filiform Lie algebras as double extensions of smaller structures.

Abstract

The aim of this work is to provide explicit calculations that describe any 7-dimensional contact nilpotent Lie algebra as a double extension of a 5-dimensional contact nilpotent Lie algebra.In particular, we describe an arbitrary (2n+1)-dimensional contact filiform Lie algebra as a double extension of a (2n-1)-dimensional contact nilpotent Lie algebra m of nilindex n by a pair (D, ).

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