代数学Cuntz-Krieger代数
Algebraic Cuntz-Krieger algebras
摘要：
我们证明了$E$是一个没有汇的有限图当且仅当Leavitt路代数$L_R(E)$同构于一个代数Cuntz-Krieger代数当且仅当$C^*$ -代数$C^*(E)$是酉的且$rank(K_0(C^*(E)))=rank(K_1(C^*(E)))$ .当$k$是域且$rank(k^{\times})< \infty$是域时，证明了Leavitt路代数$L_k(E)$同构于代数Cuntz-Krieger代数当且仅当$L_k(E)$是酉的且$rank(K_1(L_k(E)))=(rank(k^{\times})+1)rank(K_0(L_k(E)))$ .我们还证明了任何与代数Cuntz-Krieger代数Morita等价或稳定同构的单位$k$ -代数都同构于代数Cuntz-Krieger代数。因此，代数Cuntz-Krieger代数的角是代数Cuntz-Krieger代数。
英文摘要：
We show that $E$ is a finite graph with no sinks if and only if the Leavitt path algebra $L_R(E)$ is isomorphic to an algebraic Cuntz-Krieger algebra if and only if the $C^*$-algebra $C^*(E)$ is unital and $rank(K_0(C^*(E)))=rank(K_1(C^*(E)))$. When $k$ is a field and $rank(k^{\times})< \infty$, we show that the Leavitt path algebra $L_k(E)$ is isomorphic to an algebraic Cuntz-Krieger algebra if and only if $L_k(E)$ is unital and $rank(K_1(L_k(E)))=(rank(k^{\times})+1)rank(K_0(L_k(E)))$. We also show that any unital $k$-algebra which is Morita equivalent or stably isomorphic to an algebraic Cuntz-Krieger algebra, is isomorphic to an algebraic Cuntz-Krieger algebra. As a consequence, corners of algebraic Cuntz-Krieger algebras are algebraic Cuntz-Krieger algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
