Continuous subgroups of a generalized Euclidean group (Q1082457)

The general method of classification with respect to certain conjugacy of subalgebras of a finite dimensional Lie algebra L with nontrivial abelian ideal N and semisimple quotient algebra L/N is well known. The problem of classification of subalgebras of the Euclidean algebra LE(n) with respect to E(n)-conjugacy is reduced in the paper under review to the description of the irreducible parts of subalgebras of the algebra LO(n) with respect to O(n)-conjugacy. As an application of the general results, the description of the maximal abelian subalgebras of LE(n), \(n\geq 2\), and all subalgebras of LE(5) is given.