Faithful Representations of Minimal Dimension of Current Heisenberg Lie Algebras
نویسندگان
چکیده
Given a Lie algebra g over a field of characteristic zero k, let μ(g) = min{dimπ : π is a faithful representation of g}. 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 ∈ N 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 μ(hm,p) = mdeg p+ ̊
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