Faithful representations of minimal dimension of current Heisenberg Lie algebras

الأصل · EN

Given a Lie algebra g over a field of characteristic zero k, let μ(g)={ π: πis a faithful representation ofg}. Let hₘ be the Heisenberg Lie algebra of dimension 2m+1 over k and let k[t] be the polynomial algebra in one variable. Given m and p∈ k[t], let hₘ,ₚ=hₘ⊗ k[t]/(p) be the current Lie algebra associated to hₘ and k[t]/(p), where (p) is the principal ideal in k[t] generated by p. In this paper we prove that mu(hₘ,ₚ) = m °p + 2√°p.