CPA-STRUCTURE ON SMALL-DIMENSIONAL NILPOTENT LIE ALGEBRAS

Abstract

This work investigates commutative post-Lie algebra (CPA) structures on three-dimensional nilpotent Lie algebras. CPA-structures, a subset of post-Lie algebra structures, are essential for understanding the geometry of nil-affine actions and their connection to nil-affine crystallographic groups. These structures are also closely related to Poisson and Poisson-admissible algebras. By analyzing the bilinear product and the defining identities of CPA-structures, the research classifies and constructs such structures for specific three-dimensional nilpotent Lie algebras. Results provide insights into the algebraic properties and highlight areas for further exploration in higher-dimensional cases.