论文标题
函数$ k_0^{\ pereratatorname {gr}} $已满，只有弱忠诚
The functor $K_0^{\operatorname{gr}}$ is full and only weakly faithful
论文作者
论文摘要
分级分类的猜想指出，指的$ k_0^{\ propatorAtorname {gr}} $ - 组是有限图的Leavitt Path代数的完全不变的，当这些代数被视为自然分级时，由$ \ m i \ mathbb z进行自然分级。忠实于有限图的Leavitt路径代数及其分级同构的类别时，通过零组件的可逆元素进行了轭。我们表明，对于Unital Leavitt Path，可计数图的函数$ k_0^{\ operatoRatorName {gr}} $是满足的，并且仅在某些较弱的感觉中它是忠实的（Modulo指定的共轭）。
The Graded Classification Conjecture states that the pointed $K_0^{\operatorname{gr}}$-group is a complete invariant of the Leavitt path algebras of finite graphs when these algebras are considered with their natural grading by $\mathbb Z.$ The strong version of this conjecture states that the functor $K_0^{\operatorname{gr}}$ is full and faithful when considered on the category of Leavitt path algebras of finite graphs and their graded homomorphisms modulo conjugations by invertible elements of the zero components. We show that the functor $K_0^{\operatorname{gr}}$ is full for the unital Leavitt path algebras of countable graphs and that it is faithful (modulo specified conjugations) only in a certain weaker sense.
