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