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http://dx.doi.org/10.14403/jcms.2012.25.2.331

HARMONIC MAPS BETWEEN THE GROUP OF AUTOMORPHISMS OF THE QUATERNION ALGEBRA  

Kim, Pu-Young (Department of Applied Mathematics Pukyong National University)
Park, Joon-Sik (Department of Mathematics Pusan University of Foreign Studies)
Pyo, Yong-Soo (Department of Applied Mathematics Pukyong National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.25, no.2, 2012 , pp. 331-339 More about this Journal
Abstract
In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.
Keywords
harmonic map; Killing form; semisimple Lie group; invariant Riemannian metric;
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