Contractions of Exceptional Lie Algebras and Semidirect Products
نویسنده
چکیده
For any semisimple subalgebra s′ of exceptional Lie algebras s satisfying the constraint rank(s′) = rank(s)−1 we analyze the branching rules for the adjoint representation, and determine the compatibility of the components with Heisenberg algebras. The analysis of these branching rules allows to classify the contractions of exceptional algebras onto semidirect products of semisimple and Heisenberg Lie algebras. Applications to the Schrödinger algebras are given.
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 کاملIntrinsic formulae for the Casimir operators of semidirect products of the exceptional Lie algebra G2 and a Heisenberg Lie algebra
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.
متن کاملO ct 2 00 3 Extensions of Banach Lie - Poisson spaces
The extension of Banach Lie-Poisson spaces is studied and linked to the extension of a special class of Banach Lie algebras. The case of W -algebras is given particular attention. Semidirect products and the extension of the restricted Banach Lie-Poisson space by the Banach Lie-Poisson space of compact operators are given as examples.
متن کاملCanonical Maps Between Semidirect Products with Applications to Elasticity and Superfluids
It is shown that two canonical maps arising in the Poisson bracket formulations of elasticity and superfluids are particular instances of general canonical maps between duals of semidirect product Lie algebras.
متن کاملCentralizers of Lie Algebras Associated to the Descending Central Series of Certain Poly-free Groups
Poly-free groups are constructed as iterated semidirect products of free groups. The class of poly-free groups includes the classical pure braid groups, fundamental groups of fiber-type hyperplane arrangements, and certain subgroups of the automorphism groups of free groups. The purpose of this article is to compute centralizers of certain natural Lie subalgebras of the Lie algebra obtained fro...
متن کامل