What question did this study set out to answer?

To find the maximal dimension of totally geodesic subalgebras in N-graded filiform nilpotent lie algebras and confirm these dimensions can be reached.

March 29, 2026Open Access

Totally Geodesic Subalgebras of Filiform Nilpotent Lie Algebras

Key Points

To find the maximal dimension of totally geodesic subalgebras in N-graded filiform nilpotent lie algebras and confirm these dimensions can be reached.
Examine the structure of N-graded filiform nilpotent lie algebras.
Apply theoretical frameworks to analyze subalgebra dimensions.
Demonstrate existing bounds and attainability of geodesic subalgebras.
Identified the maximal dimensions for totally geodesic subalgebras.
Proved that the determined bounds can be achieved within the studied algebras.

Abstract

We determine the maximal dimension of totally geodesic subalgebras of N -graded filiform Lie algebras, and we show that these bounds are attained.

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