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Lagrange’s theorem for Hopf monoids in species
, 2012
"... Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras, ..."
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Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras,
Ppartitions and a multiparameter Klyachko idempotent
"... Because they play a role in our understanding of the symmetric group algebra, Lie idempotents have received considerable attention. The Klyachko idempotent has attracted interest from combinatorialists, partly because its definition involves the major index of permutations. For the symmetric group S ..."
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Because they play a role in our understanding of the symmetric group algebra, Lie idempotents have received considerable attention. The Klyachko idempotent has attracted interest from combinatorialists, partly because its definition involves the major index of permutations. For the symmetric group Sn, we look at the symmetric group algebra with coefficients from the field of rational functions in n variables q1,...,qn. In this setting, we can define an nparameter generalization of the Klyachko idempotent, and we show it is a Lie idempotent in the appropriate sense. Somewhat surprisingly, our proof that it is a Lie element emerges from Stanley’s theory of Ppartitions. The motivation for our work is centered around the search for Lie idempotents in the symmetric group algebra. In fact, our goal is to give a generalization of the wellknown Klyachko idempotent, and to show that important and interesting properties of the Klyachko idempotent carry over to the extended setting. It turns out that the proof that our