A quantum analog of the Poincare-Birkhoff-Witt theorem
| dc.creator | Kharchenko, Vladislav | |
| dc.date | 2000-05-10 | |
| dc.date.accessioned | 2026-07-07T04:35:10Z | |
| dc.date.available | 2026-07-07T04:35:10Z | |
| dc.description | We reduce the basis construction problem for Hopf algebras generated by skew-primitive semi-invariants to a study of special elements, called ``super-letters,'' which are defined by Shirshov standard words. In this way we show that above Hopf algebras always have sets of PBW-generators (``hard'' super-letters). It is shown also that these Hopf algebras having not more than finitely many ``hard'' super-letters share some of the properties of universal enveloping algebras of finite-dimensional Lie algebras. The background for the proofs is the construction of a filtration such that the associated graded algebra is obtained by iterating the skew polynomials construction, possibly followed with factorization. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0005101 | |
| dc.identifier | http://arxiv.org/abs/math/0005101 | |
| dc.identifier | Algebra and Logic, v.38, N4, July-August, 1999, 259-276. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59167 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17B; 16W | |
| dc.title | A quantum analog of the Poincare-Birkhoff-Witt theorem | |
| dc.type | text |