A Class of Nonunitary, Finite Dimensional Representations of the Euclidean Algebra 𝔢(2)

Abstract

In this article, we examine the finite dimensional representations of the Euclidean algebra 𝔢(2) that are obtained by embedding 𝔢(2) into 𝔰𝔩₃, the Lie algebra of traceless 3 × 3 matrices. We show that the finite dimensional, irreducible representations of 𝔰𝔩₃ restricted to 𝔢(2) are indecomposable and, when possible, we give graphical descriptions of these 𝔢(2) representations.

Key Words:

• Euclidean algebra
• Indecomposable representations
• Tensor product decomposition

Mathematics Subject Classification:

• Primary 17B10
• Secondary 17B30

Notes

Communicated by D. K. Nakano.