Algebraic Polymorphisms
| dc.creator | Schmidt, Klaus | |
| dc.creator | Vershik, Anatoly | |
| dc.date | 2007-05-25 | |
| dc.date.accessioned | 2026-07-07T08:03:13Z | |
| dc.date.available | 2026-07-07T08:03:13Z | |
| dc.description | In this paper we consider a special class of polymorphisms with invariant measure, - (cf.[1])- the algebraic polymorphisms of compact groups. A general polymorphism is -- by definition -- a many-valued map with invariant measure, and the conjugate operator of a polymorphism is a Markov operator (i.e., a positive operator on $L^2$ of norm 1 which preserves the constants). In the algebraic case a polymorphism is a correspondence in the sense of algebraic geometry, but here we investigate it from a dynamical point of view. The most important examples are the algebraic polymorphisms of torus, where we introduce a parametrization of the semigroup of toral polymorphisms in terms of rational matrices and describe the spectra of the corresponding Markov operators. | |
| dc.description | 9 p.,Ref 1 | |
| dc.identifier | https://arxiv.org/abs/0705.3706 | |
| dc.identifier | http://arxiv.org/abs/0705.3706 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129495 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Algebraic Topology | |
| dc.subject | 37A05,28D05,15A36 | |
| dc.title | Algebraic Polymorphisms | |
| dc.type | text |