一个Gelfand-Kirillov维数1的Hopf代数的例子

An Example of Hopf Algebras of Gelfand-Kirillov Dimension 1

构建了一个Gelfand-Kirillov维数1的Hopf代数的例子.从而证明,除了无限循环群的群代数kΖ、无限二面体群的群代数kD和无限维Taft代数外,还存在其他的诺特、仿射、正则、素的Gelfand-Kirillov维数1的Hopf代数.

This paper defines a new algebra A（n,q）,and proves that A（n,q） is a Noetherian,affine,regular and prime Hopf algebra of Gelfand-Kirillov dimension 1 and hence gives an answer to an open question： Infinite cyclic group algebra kΖ、infinite dihedral group and infinite dimensional Taft algebras are examples of affine prime regular Hopf algebras of GK-dimension 1.