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|Type:||Artigo de periódico|
|Title:||Ideals of identities of representations of nilpotent Lie algebras|
|Abstract:||Let L be a Lie algebra, nilpotent of class 2, over an infinite field It, and suppose that the centre C of L is one dimensional; such Lie algebras are called Heisenberg algebras. Let rho:L --> hom(K) V be a finite dimensional representation of the Heisenberg algebra L such that rho(C) contains non-singular linear transformations of V, and denote I(rho) the ideal of identities for the representation rho. We prove that the ideals of identities of representations containing I(rho) and generated by multilinear polynomials satisfy the ACC. Let sl(2)(K) be the Lie algebra of the traceless 2 x 2 matrices over K, and suppose the characteristic of K equals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation of sl(2)(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras lover an infinite field of characteristic 2) that contain the identities of the regular representation of sl(2)(K).|
identities of representations of Lie algebras
|Editor:||Marcel Dekker Inc|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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