一类张量代数的商代数的研究

On a Class of Quotient Algebras of Tensor Algebras

主要研究了一类典型张量代数商代数Αδ的基。利用归纳法,构造了一个与Αδ相关的结合代数Λδ,并用初等的方法详细证明了Λδ乘法的合理性。通过建立一个Αδ到Λδ的代数同态,给出Αδ基元素的具体表达形式满足一定顺序关系的单项式。

The basis of a typical quotient algebra Aδof tensor algebra are studied.By mathematical induction,an associated algebraΛδthat is related to Aδis constructed and the multiplication ofΛδis proved to be well-defined in an elementary way.Finally,the basis is obtained by using a homomorphism fromΑδtoΛδ,the specific form of a basis ofΑδare given:they are monomials that satisfying certain ordinal relations.