Verbal ideals and unobstructed complex parallelisable nilmanifolds

Autor:	Paulsen, Matthias, Rollenske, Sönke, Wehler, Konstantin
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry Mathematics - Rings and Algebras 32G05 (Primary) 17B01 17B30 32M10 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We show that a compact complex parallelisable nilmanifold has unobstructed deformations if and only if its associated Lie algebra satisfies a reality condition and is a free Lie algebra in a variety of Lie algebras, that is, defined by a verbal ideal in a free Lie algebra. We provide a partial classification of verbal ideals and show that there are finitely many such Lie algebras up to dimension 19, whereas infinite families start to appear in dimension 20. As a consequence, there are finitely many complex homotopy types of unobstructed complex parallelisable nilmanifolds up to dimension 19, and infinitely many in dimension 20. Comment: 18 pages; comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.17560 Zobrazit plný text záznamu View this record from Arxiv