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Wildness in the product groups

G. Hjorth (2000)

Fundamenta Mathematicae

Non-abelian Polish groups arising as countable products of countable groups can be tame in arbitrarily complicated ways. This contrasts with some results of Solecki who revealed a very different picture in the abelian case.

Witt algebra and the curvature of the Heisenberg group

Zoltán Muzsnay, Péter T. Nagy (2012)

Communications in Mathematics

The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.

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