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A quantum analog of the PoincareBirkhoffWitt theorem
 V. K. Kharchenko
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We reduce the basis construction problem for character Hopf algebras to a study of special elements, called “superletters,” which are defined by Shirshov standard words. It is shown that character Hopf algebras having not more than finitely many “hard” superletters share some of the properties of universal envelopings of finitedimensional 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.
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 Title
 A quantum analog of the PoincareBirkhoffWitt theorem
 Journal

Algebra and Logic
Volume 38, Issue 4 , pp 259276
 Cover Date
 19990701
 DOI
 10.1007/BF02671731
 Print ISSN
 00025232
 Online ISSN
 15738302
 Publisher
 Springer US
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