论文标题
$ \ MATHBB {Z} $ - Grassmann代数的分级多项式身份
$\mathbb{Z}$-graded polynomial identities of the Grassmann algebra
论文作者
论文摘要
让$ f $是一个与2不同的特征性的无限领域，让$ e $为无限尺寸$ f $ -vector-vector Space $ l $的Grassmann代数。在本文中，我们研究了$ \ mathbb {z} $ - 相对于某些$ \ mathbb {z} $的分级多项式身份，以使矢量空间$ l $在等级中是同质的。更确切地说，我们构造了$ e $的三种类型的$ \ mathbb {z} $ - 由$ e^{\ infty} $表示，$ e^{\ eftty} $，$ e^{k^\ ast} $和$ e^{k} $，我们给出了相应的$ \ mathbb {z} $ nnial nife的明确形式。我们表明，可以从\ cite {disil}中研究的同质超级$ e _ {\ infty} $，$ e_ {k^\ ast} $和$ e_ {k {k {k {k {k {k {k} $可以从$ e^{\ e^{\ effty} $ e^{\ e^{此外，我们还展示了其他几种类型的同质$ \ mathbb {z} $ - $ e $的等级，并描述其分级身份。
Let $F$ be an infinite field of characteristic different from 2, and let $E$ be the Grassmann algebra of an infinite dimensional $F$-vector space $L$. In this paper we study the $\mathbb{Z}$-graded polynomial identities of $E$ with respect to certain $\mathbb{Z}$-grading such that the vector space $L$ is homogeneous in the grading. More precisely, we construct three types of $\mathbb{Z}$-gradings on $E$, denoted by $E^{\infty}$, $E^{k^\ast}$ and $E^{k}$, and we give the explicit form of the corresponding $\mathbb{Z}$-graded polynomial identities. We show that the homogeneous superalgebras $E_{\infty}$, $E_{k^\ast}$ and $E_{k}$ studied in \cite{disil} can be obtained from $E^{\infty}$, $E^{k^\ast}$ and $E^{k}$ as quotient gradings. Moreover we exhibit several other types of homogeneous $\mathbb{Z}$-gradings on $E$, and describe their graded identities.
