Left Invariant Metrics on Lie Groups Associated with G-Associative Algebras

Key Points

• The aim is to explore left invariant metrics on Lie groups linked to G-associative algebras and classify them.
• Develop a left invariant connection associated with a left invariant metric on Lie groups.
• Utilize an algebraic approach related to Lie-admissible algebras.
• Classify metrics in low dimensions for specific subclasses of Lie-admissible Lie algebras.
• Classifications of left invariant metrics on Lie groups associated with G-associative algebras are presented.
• Findings contribute to understanding the structure of Lie groups in a broader algebraic framework.