The Principal Element of a Frobenius Lie Algebra

    loading  Checking for direct PDF access through Ovid

Abstract

We introduce the notion of the principal element of a Frobenius Lie algebra 𝔣. The principal element corresponds to a choice of E ∈ such that F[–, –] non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to sln, its eigenvalues are integers and are independent of F. For certain “small” functionals F, a simple construction is given which readily yields the principal element. When applied to the first maximal parabolic subalgebra of sln, the principal element coincides with semisimple element of the principal three-dimensional subalgebra. We also show that Frobenius algebras are stable under deformation.

Related Topics

    loading  Loading Related Articles