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TOWARDS UNIQUENESS OF MPR, THE MALVENUTO-POITIER-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
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  • Journal title : Honam Mathematical Journal
  • Volume 29, Issue 2,  2007, pp.119-192
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2007.29.2.119
 Title & Authors
TOWARDS UNIQUENESS OF MPR, THE MALVENUTO-POITIER-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
Hazewinkel, Michiel;
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 Abstract
A very important Hopf algebra is the graded Hopf algebra Symm of symmetric functions. It can be characterized as the unique graded positive selfdual Hopf algebra with orthonormal graded distinguished basis and just one primitive element from the distinguished basis. This result is due to Andrei Zelevinsky. A noncommutative graded Hopf algebra of this type cannot exist. But there is a most important positive graded Hopf algebra with distinguished basis that is noncommutative and that is twisted selfdual, the Malvenuto-Poirier-Reutenauer Hopf algebra of permutations. Thus the question arises whether there is a corresponding uniqueness theorem for MPR. This prepreprint records initial investigations in this direction and proves that uniquenees holds up to and including the degree 4 which has rank 24.
 Keywords
Hopf algebra;Hopf algebra of symmetric functions;MPR;Hopf algebra of permutations;Malvenuto-Poirier-Reutenauer Hopf algebra;PSH algebra;PtwSH algebra;Zelevinsky theorem;uniqueness theorem;rigidity theorem;
 Language
English
 Cited by
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