函数代数中的无穷小不变量

摘要：

设G是正特征代数闭域上的约化连通线性代数群，g是它的李代数.首先，我们将半单群的Picard群的一个著名结果推广到约化群。证明了：若导群是单连通的，且g满足一个弱条件，则G上由在g的作用下不变的正则函数构成的代数K[G]^g是唯一的因子分解整环.

英文摘要：

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we extend a well-known result about the Picard group of a semisimple group to reductive groups. Then we prove that, if the derived group is simply connected and g satisfies a mild condition, the algebra K[G]^g of regular functions on G that are invariant under the action of g derived from the conjugation action, is a unique factorisation domain.

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