论文标题
多项式身份，代数为3 $ \ times $ 3上三角矩阵的多项式身份
Polynomial identities with involution for the algebra of 3 $\times$ 3 upper triangular matrices
论文作者
论文摘要
令$ \ mathbb {f} $为特征$ p $的字段，让$ ut_n（\ mathbb {f}）$为$ n $ n $ times n $上三角矩阵的代数，超过$ \ mathbb {f} $。在本文中，我们描述了：$ ut_n（\ mathbb {f}）$的所有$*$ - 中央多项式的集合，当$ n \ geq 3 $和$ p \ neq 2 $时； $ ut_3（\ Mathbb {f}）$的所有$*$ - 多项式身份的集合，当$ \ mathbb {f} $是无限的，$ p> 2 $。
Let $\mathbb{F}$ be a field of characteristic $p$, and let $UT_n(\mathbb{F})$ be the algebra of $n \times n$ upper triangular matrices over $\mathbb{F}$ with an involution of the first kind. In this paper we describe: the set of all $*$-central polynomials for $UT_n(\mathbb{F})$ when $n\geq 3$ and $p\neq 2$ ; the set of all $*$-polynomial identities for $UT_3(\mathbb{F})$ when $\mathbb{F}$ is infinite and $p>2$.
