Geometry, Gravity and Supersymmetry

Rigidity of 2-step Carnot algebras

26 Apr 2017, 11:05

45m

02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

Speaker

Prof. Boris Kruglikov (University of Tromsø)

Description

We study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo $H$- and $J$-type algebras are given. In particular, we establish the relation of the so-called $J^2$-condition to rigidity, and we explore these conditions in relation to pseudo $H$-type algebras. Based on work [(arXiv:1603.00373 [math.RT])][1] with Mauricio Godoy-Molina, Irina Markina and Alexander Vasil'ev. [1]: https://arxiv.org/abs/1603.00373

Presentation materials

Slides

Boris.pdf