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Let l, n ∈ N. Let sp 2l be the symplectic Lie algebra over the complex number field C. Let V be the natural representation of the quantized enveloping algebra U q (sp 2l ) and B n,q the specialized Birman-Murakami-Wenzl algebra with parameters −q 2l+1 , q.In this paper, we construct a certain element in the annihilator of V ⊗n in B n,q , which comes from some one-dimensional twosided ideal of Birman-Murakami-Wenzl algebra and is explicitly characterized (modulo the determination of some constants). We prove that the two-sided ideal generated by this element is indeed the whole annihilator of V ⊗n in B n,q and conjecture that the same is true over arbitrary ground fields and for any specialization of the parameter q. The conjecture is verified in the case when q is specialized to 1 (i.e., the Brauer algebra case) and the case when n = l + 1.Crown

Motivated by the powerful and elegant works of Miers (1971Miers ( , 1973Miers ( , 1978 we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let A be a von Neumann algebra without abelian central summands of type I1. It is shown that every nonlinear Lie n-derivation of A has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each (n − 1)th commutator of A. Several potential research topics related to our work are also presented.

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