q-Heisenberg代数的Gröbner-Shirshov基及结构性质

Gröbner-Shirshov Basis and Structural Properties of q-Heisenberg Algebra

设n是正整数,q是非零的复数,h_(n)(q)是q-Heisenberg代数.首先通过计算拟交换关系间的所有合成给出了h_(n)(q)的极小Gröbner-Shirshov基,并取关于此Gröbner-Shirshov基的不可约元素构造了h_(n)(q)的PBW基,然后证明了h_(n)(q)的一些结构性质.

Let n be a positive integer,q a non-zero complex number,and h_(n)(q)a q-Heisenberg algebra.In this paper,we first give the minimal Gröbner-Shirshov basis of h_(n)(q)by calculating all the compositions between the skew commutator relations,and construct the PBW basis of h_(n)(q)by taking the irreducible elements about this Gröbner-Shirshov basis.Then we prove some structural properties of h_(n)(q).