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.