Cyclotomic completions of polynomial rings
| dc.creator | Habiro, Kazuo | |
| dc.date | 2002-09-24 | |
| dc.date.accessioned | 2026-07-07T04:51:12Z | |
| dc.date.available | 2026-07-07T04:51:12Z | |
| dc.description | The main object of study in this paper is the completion Z[q]^N=\varprojlim_n Z[q]/((1-q)(1-q^2)...(1-q^n)) of the polynomial ring Z[q], which arises from the study of a new invariant of integral homology 3-spheres with values in Z[q]^N announced by the author, which unifies all the sl_2 Witten-Reshetikhin-Turaev invariants at various roots of unity. We show that any element of Z[q]^N is uniquely determined by its power series expansion in q-ζfor each root ζof unity. We also show that any element of Z[q]^N is uniquely determined by its values at the roots of unity. These results may be interpreted that Z[q]^N behaves like a ring of ``holomorphic functions defined on the set of the roots of unity''. We will also study the generalizations of Z[q]^N, which are completions of the polynomial ring R[q] over a commutative ring R with unit with respect to the linear topologies defined by the principal ideals generated by products of powers of cyclotomic polynomials. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209324 | |
| dc.identifier | http://arxiv.org/abs/math/0209324 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65059 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Quantum Algebra | |
| dc.subject | 13B35; 13B25; 57M27 | |
| dc.title | Cyclotomic completions of polynomial rings | |
| dc.type | text |