호남수학학술지 (Honam Mathematical Journal)

  • 제29권4호
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  • Pages.495-509
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  • 2007
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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RIGIDITY FOR MPR, THE MALVENUTO-POIRIER-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS

  • 투고 : 2006.06.27
  • 심사 : 2006.08.05
  • 발행 : 2007.12.25
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초록

In this note it is proved that MPR is rigid as a Hopf algebra with distinguished basis. I.e. there are no nontrivial automorphisms that preserve the multiplication and comultiplication and take the distinguished basis of all permutations into itself (as a graded set).

키워드

참고문헌

  1. Marcelo Aguiar, Frank Sottile, Structure of the Malvenuto-Reutenauer Hopf algebra of permutations, Preprint, Dept. Math. Texas A&M University, Dept. Math., University of Massachusetts at Amherst., 2002.
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