Zeta functions of discrete groups acting on trees. (English) Zbl 1013.11057
Here work of H. Bass [Ihara-Selberg zeta function of a tree lattice, Int. J. Math. 3, 717-797 (1992; Zbl 0767.11025)] for finite graphs is generalized to the infinite case assuming certain finiteness conditions. The theory of von Neumann algebras, as well as representations and determinants of Hilbert modules is required. The paper concludes with examples such as the infinite grid.
Reviewer: Audrey A.Terras (La Jolla)
MSC:
| 11M41 | Other Dirichlet series and zeta functions |
| 20E08 | Groups acting on trees |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 46L99 | Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) |
Citations:
Zbl 0767.11025References:
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