受限群代数的空间离散化
Spatial discretization of restricted group algebras
AI总结：
本文通过有限截面方法研究有限生成离散群的受限群代数的空间离散化，重点分析了有限截面序列生成的代数的拟交换子理想及其序列稳定性，并证明了交换群和自由非交换群的有限截面序列代数是分形的。
摘要：
我们考虑通过有限截面方法对有限生成离散群的受限群代数进行空间离散化，该代数通过其左正则表示具体化为一个算子代数。特别关注由有限截面序列生成的代数的拟交换子理想以及该代数中序列的稳定性。对于这两个问题，离散边界的序列起着关键作用。最后，对于交换群和自由非交换群，有限截面序列代数被证明是分形的。
英文摘要：
We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special emphasis is paid to the quasicommutator ideal of the algebra generated by the finite sections sequences and to the stability of sequences in that algebra. For both problems, the sequence of the discrete boundaries plays an essential role. Finally, for commutative groups and for free non-commutative groups, the algebras of the finite sections sequences are shown to be fractal.
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。
