标题： 斜原始元素代数 显示英文标题

标题： An Algebra of Skew Primitive Elements

摘要： 我们研究由阿贝尔群的群元素的斜初等半不变量生成的霍普夫代数的斜初等元素集上的各种项运算。所有1-线性二元运算都被描述，而三线性和四线性运算得到了详细的处理。多线性运算存在的必要且充分条件以特定非交换多项式的线性相关性以及一个算术条件来表述。我们将这个条件导致相关多项式线性相关的猜想称为猜想，并认为该条件本身是充分的（有关此猜想的证明，请参见《多线性量子运算的存在条件》，《代数杂志》，217，1999，188-228）。 显示英文摘要

摘要： We study the various term operations on the set of skew primitive elements of Hopf algebras, generated by skew primitive semi-invariants of an Abelian group of grouplike elements. All 1-linear binary operations are described and trilinear and quadrilinear operations are given a detailed treatment. Necessary and sufficient conditions for the existence of multilinear operations are specified in terms of the property of particular noncommutative polynomials being linearly dependent and of one arithmetic condition. We dub the conjecture that this condition implies, in fact, the linear dependence of the polynomials in question and so is itself sufficient (a proof of this conjecture see in "An existence condition for multilinear quantum operations," Journal of Algebra, 217, 1999, 188-228).