on four-dimensional Lie groups
Author: María Laura Barberis
Journal: Proc. Amer. Math. Soc. 125 (1997), 1043-1054
MSC (1991): Primary 32M10, 53C25, 53C56; Secondary 32M15, 53C55
MathSciNet review: 1353375
Abstract: The purpose of this paper is to classify invariant hypercomplex structures on a -dimensional real Lie group . It is shown that the -dimensional simply connected Lie groups which admit invariant hypercomplex structures are the additive group of the quaternions, the multiplicative group of nonzero quaternions, the solvable Lie groups acting simply transitively on the real and complex hyperbolic spaces, and , respectively, and the semidirect product . We show that the spaces and possess an of (inequivalent) invariant hypercomplex structures while the remaining groups have only one, up to equivalence. Finally, the corresponding hyperhermitian -manifolds are determined.
María Laura Barberis
Affiliation: FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 - Córdoba, Argentina
Address at time of publication: Department of Mathematics, University of California at San Diego, La Jolla, California 92093
Email: firstname.lastname@example.org, email@example.com
Keywords: Hypercomplex structure (hcs), hyperhermitian metric
Received by editor(s): March 9, 1994
Received by editor(s) in revised form: September 5, 1995
Additional Notes: The author was partially supported by Conicor and Conicet (Argentina).
Communicated by: Roe Goodman
Article copyright: © Copyright 1997 American Mathematical Society