论文标题
差分身份的增长
Growth of differential identities
论文作者
论文摘要
在本文中，我们研究了某些代数的差异身份的增长，即衍生物，即联想代数，其中lie代数$ l $（及其通用包围的代数$ u（l）$）通过衍生作用。特别是，我们详细研究了某些代数的差异身份和共同序列的差异序列具有多项式生长。此外，我们将完整描述代数$ ut_2 $ $ 2 \ times 2 $上三角矩阵的差分身份，并通过派生来赋予Lie代数的所有可能作用。最后，我们介绍了无限尺寸格拉斯曼$ g $的差分身份的结构，就有限的尺寸谎言谎言代数$ l $ $ l $。
In this paper we study the growth of the differential identities of some algebras with derivations, i.e., associative algebras where a Lie algebra $L$ (and its universal enveloping algebra $U(L)$) acts on them by derivations. In particular, we study in detail the differential identities and the cocharacter sequences of some algebras whose sequence of differential codimensions has polynomial growth. Moreover, we shall give a complete description of the differential identities of the algebra $UT_2$ of $2\times 2$ upper triangular matrices endowed with all possible action of a Lie algebra by derivations. Finally, we present the structure of the differential identities of the infinite dimensional Grassmann $G$ with respect to the action of a finite dimensional Lie algebra $L$ of inner derivations.
