Nonlinear oblique projections

TL;DR

This paper introduces nonlinear oblique projections within nilpotent Lie algebras, demonstrating their real analytic properties on Schubert cells, which advances the understanding of algebraic and geometric structures in this context.

Contribution

It constructs nonlinear oblique projections using the Baker-Campbell-Hausdorff multiplication and proves their real analyticity on Schubert cells.

Findings

Proved nonlinear projections are real analytic on Schubert cells.

Constructed projections explicitly via Baker-Campbell-Hausdorff multiplication.

Enhanced understanding of subalgebra structures in nilpotent Lie algebras.

Abstract

We construct nonlinear oblique projections along subalgebras of nilpotent Lie algebras in terms of the Baker-Campbell-Hausdorff multiplication. We prove that these nonlinear projections are real analytic on every Schubert cell of the Grassmann manifold whose points are the subalgebras of the nilpotent Lie algebra under consideration.