solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看3744次
Leavitt path algebras of Cayley graphs $C_n^j$. (arXiv:1712.06480v1 [math.RA])
来源于:arXiv
Let $n$ be a positive integer. For each $0\leq j \leq n-1$ we let $C_n^j$
denote the Cayley graph of the cyclic group $\mathbb{Z}_n$ with respect to the
subset $\{1,j\}$. Utilizing the Smith Normal Form process, we give an explicit
description of the Grothendieck group of each of the Leavitt path algebras
$L_K(C_n^j)$ for any field $K$. Our general method significantly streamlines
the approach that was used in previous work to establish this description in
the specific case $j=2$. Along the way, we give necessary and sufficient
conditions on the pairs $(j,n)$ which yield that this group is infinite. We
subsequently focus on the case $j = 3$, where the structure of this group turns
out to be related to a Fibonacci-like sequence, called the Narayana's Cows
sequence. 查看全文>>