论文标题
U（u（u（2））中央延伸的非共同几何形状）
Noncommutative geometry on central extension of U(u(2))
论文作者
论文摘要
在以前的出版物中，我们在代数U（GL（n））上引入了部分衍生物的类似物。在本文中，我们比较了引入这些类似物的两种方法：通过所谓的量子双打和通过结构结构。在n = 2的情况下，我们从u（u（u（2））扩展了量子部分衍生物（代数u（gl（2））的紧凑形式）在较大的代数上，分为两个步骤。首先，我们在该代数的中心扩展上定义了衍生物，然后通过使用Cayley-Hamilton身份来对某些具有非交通性条目的矩阵，以相应的偏斜场的某些元素延长它们。讨论了这种差分计算的最终应用。
In our previous publications we have introduced analogs of partial derivatives on the algebras U(gl(N)). In the present paper we compare two methods of introducing these analogs: via the so-called quantum doubles and by means of a coalgebraic structure. In the case N=2 we extend the quantum partial derivatives from U(u(2)) (the compact form of the algebra U(gl(2))) on a bigger algebra, constructed in two steps. First, we define the derivatives on a central extension of this algebra, then we prolongate them on some elements of the corresponding skew-field by using the Cayley-Hamilton identities for certain matrices with noncommutative entries. Eventual applications of this differential calculus are discussed.
