Quantum octonions

Abstract

This paper constructs a quantum deformation of the complex Cayley dgebra. The method uses the representation theory of U _q(sl(2)), the quantized enveloping algebra of the simple complex Lie algebra s/(2). The paper begins by constructing a quantum deforma-tion of the complex quaternion algebra, since this simpler case illustrates all of the necessary steps. As intermediate results, deformations are constructed of sl(2) and the 7-dimensional simple Malcev algebra.