$\mathbb{Z}$ 上 Leavitt 路径代数的 $*$-同构
环与代数
2018-04-12 v3 算子代数
摘要
我们通过证明两个任意可数有向图在 上的 Leavitt 路径代数 -同构当且仅当相应的图群胚同构（当且仅当相应的图 -代数之间存在保对角的同构），来刻画它们何时 -同构。我们还证明，任意两个 上的 Leavitt 路径代数之间的 -同态将对角映到对角。这两个结果对 的较 稍更一般的子环也成立。
引用
@article{arxiv.1601.00777,
title = {$*$-isomorphism of Leavitt path algebras over $\mathbb{Z}$},
author = {Toke Meier Carlsen},
journal= {arXiv preprint arXiv:1601.00777},
year = {2018}
}
备注
9 pp. Thm 1 and Cor 5 have been changed to emphasize that the *-homomorphisms are *-algebra homomorphisms. The references [6], [10], [12] and [21] have been added, and the remarks following Thm 1 have been updated in order to reflect new results in these papers. There is no longer any Remark 4, so Prop 5 has become Prop 4, and Cor 6 has become Cor 5. This is the version that will be published