A quantum analog of the Poincare-Birkhoff-Witt theorem
- Cite this article as:
- Kharchenko, V.K. Algebr Logic (1999) 38: 259. doi:10.1007/BF02671731
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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.