论文标题
在莱维特路径代数的格罗伦迪克群体之间提起形态
Lifting morphisms between graded Grothendieck groups of Leavitt path algebras
论文作者
论文摘要
我们表明，任何指向的，预定的模块映射$ \ mathfrak {bf} _ {\ mathrm {gr}}（e）\ to \ mathfrak {bf} _ {\ mathrm {gr {gr ^}} $ $ \ ast $ -HOMORPHISM $ l_ \ ell（e）\ to l_ \ ell（f）$在相应的Leavitt路径代数之间在任何交换UNITAL RING上，带有互惠$ \ ell $。当$ \ ell $是一个字段时，我们专门研究案例，我们建立了Hazrat关于Leavitt Path $ \ ell $ -Algebras of Leavitt Path $ \ ell $ -Algebras的富裕部分，并用订单单位将$ l_ \ ell（e）$降低的模块进行预订的模块。我们的升降机的建设是合并性质的；我们将这种结构产生的地图描述为沿$ \ ell $的标量扩展，分级$ \ ast $ -Homomorphisms $ l _ {\ Mathbb z}（e）\ to l _ {\ Mathbb Z}（\ Mathbb z}（f）（f）保存在此处介绍了一个sub-$ \ ast $ - $ - $ - $ - semeriring。
We show that any pointed, preordered module map $\mathfrak{BF}_{\mathrm{gr}}(E) \to \mathfrak{BF}_{\mathrm{gr}}(F)$ between Bowen-Franks modules of finite graphs can be lifted to a unital, graded, diagonal preserving $\ast$-homomorphism $L_\ell(E) \to L_\ell(F)$ between the corresponding Leavitt path algebras over any commutative unital ring with involution $\ell$. Specializing to the case when $\ell$ is a field, we establish the fullness part of Hazrat's conjecture about the functor from Leavitt path $\ell$-algebras of finite graphs to preordered modules with order unit that maps $L_\ell(E)$ to its graded Grothendieck group. Our construction of lifts is of combinatorial nature; we characterize the maps arising from this construction as the scalar extensions along $\ell$ of unital, graded $\ast$-homomorphisms $L_{\mathbb Z}(E) \to L_{\mathbb Z}(F)$ that preserve a sub-$\ast$-semiring introduced here.
