论文标题
自由双协代代数的不变理论
Invariant theory of free bicommutative algebras
论文作者
论文摘要
双方代数的种类包括满足右 - 和左征服性的多项式身份$（x_1x_2）x_3 =（x_1x_3）x_2 $和$ x_1（x_2x_3）= x_2（x_2（x_2（x_2）（x_1x_1x_3）$。令$ f_d $为特征的字段$ k $ 0。当$ g $是有限的时，我们搜索作用于多项式代数的有限群体的经典结果的类比：艾米·诺瑟（Emmy Noether）的Endlichkeitssatz，Molien公式和Chevalley-Shephard-todd定理，并显示了Bicomurtative algeberas的相似性和差异。我们还描述了$ f_d $中的对称多项式。
The variety of bicommutative algebras consists of all nonassociative algebras satisfying the polynomial identities of right- and left-commutativity $(x_1x_2)x_3=(x_1x_3)x_2$ and $x_1(x_2x_3)=x_2(x_1x_3)$. Let $F_d$ be the free $d$-generated bicommutative algebra over a field $K$ of characteristic 0. We study the algebra $F_d^G$ of invariants of a subgroup $G$ of the general linear group $GL_d(K)$. When $G$ is finite we search for analogies of classical results of invariant theory of finite groups acting on polynomial algebras: the Endlichkeitssatz of Emmy Noether, the Molien formula and the Chevalley-Shephard-Todd theorem and show the similarities and the differences in the case of bicommutative algebras. We also describe the symmetric polynomials in $F_d$.
