Intrinsic formulae for the Casimir operators of semidirect products of the exceptional Lie algebra G2 and a Heisenberg Lie algebra
نویسنده
چکیده
We show that the Casimir operators of the semidirect products G2 ⊕2Γ(a,b)⊕Γ(0,0)h of the exceptional Lie algebra G2 and a Heisenberg algebra h can be constructed explicitly from the Casimir operators of G2.
منابع مشابه
Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
Given a semidirect product g = s ⊎ r of semisimple Lie algebras s and solvable algebras r, we construct polynomial operators in the enveloping algebra U(g) of g that commute with r and transform like the generators of s, up to a functional factor that turns out to be a Casimir operator of r. Such operators are said to generate a virtual copy of s in U(g), and allow to compute the Casimir operat...
متن کاملLattice of full soft Lie algebra
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a ...
متن کاملOn dimensions of derived algebra and central factor of a Lie algebra
Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.
متن کاملDouble derivations of n-Lie algebras
After introducing double derivations of $n$-Lie algebra $L$ we describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual derivation Lie algebra $mathcal Der(L)$. In particular, we prove that the inner derivation algebra $ad(L)$ is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra wit...
متن کاملA Bound for the Nilpotency Class of a Lie Algebra
In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.
متن کامل