有限维Leavitt路代数的分次双代数结构

The Graded Bialgebras Structure ofFinite Dimensional Leavitt Path Algebras

基于Leavitt路代数的整数分次结构,给出了具有单位元且是代数同态的余单位定义的共性:只存在一个顶点,使得余单位在此处定义为1,而在其余顶点处的定义均为0.特别地,对于有限维Leavitt路代数,满足前述共性的顶点是孤立点.构造基元处的余乘定义,证明了:有限维Leavitt路代数具有整数分次双代数结构当且仅当其底图含有孤立点.

On the basis of the Z-graded algebra structure on a Leavitt path algebra,this paper presents the common feature of the definition of a counit map that satisfies the identity element and is an algebra homomorphism:there exists only one vertex,such that the counit map is 1 under its definition,and the definition of the rest vertices is 0.In particular,for dimensional Leavitt path algebras,the vertices which satisfy the above commonality are isolated points.Then the definition of the comultiplication map is constructed at the primitive.It is proved that a finite dimensional Leavitt path algebra has a Z-graded bialgebra structure if and only if the underlying graph has isolated vertices.