, Volume 38, Issue 4, pp 259-276

A quantum analog of the Poincare-Birkhoff-Witt theorem

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Abstract

We reduce the basis construction problem for character Hopf algebras to a study of special elements, called “super-letters,” which are defined by Shirshov standard words. It is shown that character Hopf algebras having not more than finitely many “hard” super-letters share some of the properties of universal envelopings of finite-dimensional lie algebras. The background for our 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.

Supported by the National Society of Researchers, México (SNI, exp. 18740, 1997–2000)
Translated fromAlgebra i Logika, Vol. 38, No. 4, pp. 476–507, July–August, 1999.