论文标题
$ \ mathbb {z} _2 $ - $ 2 \ times 2 $上三角矩阵的约旦代数的多项式身份
$\mathbb{Z}_2$-graded polynomial identities for the Jordan algebra of $2\times 2$ upper triangular matrices
论文作者
论文摘要
令$ k $为char $（k）\ neq 2 $的字段（有限或无限），让$ ut_n = ut_n（k）$为$ n \ times n $ times n $ times n $ times n $ tires n $上三角矩阵代数超过$ k $。如果$ \ cdot $是$ ut_n $上的常规产品，则使用新产品$ a \ circ b =（1/2）（a \ cdot b +b +b \ cdot a）$我们有$ ut_n $是jordan代数，由$ uj_n = uj_n（k）$表示。在本文中，我们描述了所有$ \ mathbb {z} _2 $ - $ uj_2 $的多项式身份，并使用任何非平凡$ \ mathbb {z} _2 $ grading。此外，我们描述了相对免费的$ \ mathbb {z} _2 $ graded代数的线性基础。
Let $K$ be a field (finite or infinite) of char$(K)\neq 2$ and let $UT_n=UT_n(K)$ be the $n\times n$ upper triangular matrix algebra over $K$. If $\cdot $ is the usual product on $UT_n$ then with the new product $a\circ b=(1/2)(a\cdot b +b\cdot a)$ we have that $UT_n$ is a Jordan algebra, denoted by $UJ_n=UJ_n(K)$. In this paper, we describe the set of all $\mathbb{Z}_2$-graded polynomial identities of $UJ_2$ with any nontrivial $\mathbb{Z}_2$-grading. Moreover, we describe a linear basis for the corresponding relatively free $\mathbb{Z}_2$-graded algebra.
