Embeddings of the Euclidean algebra e(3) into sl(4, C) and restrictions of irreducible representations of sl(4, C)

摘要

The Euclidean group E(3) is the Lie group of orientation-preserving isometries of three-dimensional Euclidean space. It is the noncompact, semidirect product group E(3) congruent to SO(3) proportional to R-3. The Euclidean algebra e(3) is the complexification of the Lie algebra of E(3). We classify the embeddings of the Euclidean algebra e(3) into the simple Lie algebra sl(4, C) and, as an application of this classification, discuss the restriction to various embeddings of e(3) of certain irreducible representations of sl(4, C). In particular, we consider which of these restrictions are e(3)-indecomposable. (C) 2011 American Institute of Physics. [doi:10.1063/1.3531984]