CR embeddings of nilpotent Lie groups

TL;DR

This paper demonstrates that certain nilpotent Lie groups with specific complex structures can be embedded into complex space as edges of wedges, using polynomial-defined complex domains.

Contribution

It introduces a method for CR embedding of nilpotent Lie groups with integrable complex structures into complex spaces as edges of wedges.

Findings

CR embeddings exist for these Lie groups

Embedding is realized via polynomial-defined complex domains

The approach generalizes previous embedding techniques

Abstract

We show that a connected, simply connected nilpotent Lie group with an integrable left-invariant complex structure on a generating and suitably complemented subbundle of the tangent bundle admits a CR embedding in complex space as the edge of a wedge in a complex domain defined by polynomials.