Primary decomposition in enveloping algebras

Enveloping Algebras of Hom-lie Algebras

A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...

Coloured quantum universal enveloping algebras

We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called colour group. Such transformations are labelled by some colour parameters, taking values in a colour set C. We show that vario...

More Tight Monomials in Quantized Enveloping Algebras

Delta Methods in Enveloping Algebras of Lie Colour Algebras

In recent papers J. Bergen and D. S. Passman have applied so-called`Delta methods' to enveloping algebras of Lie superalgebras. This paper generalizes their results to the class of Lie colour algebras. The methods and results in this paper are very similar to those of Bergen and Passman, and many of their proofs generalize easily. However, at some points there are serious diiculties to overcome...

Fox-type Problems in Enveloping Algebras

Let L be a Lie algebra with the universal enveloping algebra U(L). The augmentation ideal ω(L) of U(L) is the associative ideal of U(L) generated by L. Let S be a subalgebra of L and n a positive integer. In this paper we prove that L ∩ ω(L)ω(S) = γn+2(S) + γn+1(S∩γ2(L)), where γn+2(S) is the (n+2) term of the lower central series of S.