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Natural endomorphisms of quasi-shuffle Hopf algebras

Jean-Christophe Novelli, Frédéric Patras, Jean-Yves Thibon (2013)

Bulletin de la Société Mathématique de France

The Hopf algebra of word-quasi-symmetric functions ( 𝐖𝐐𝐒𝐲𝐦 ), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the other operations on 𝐖𝐐𝐒𝐲𝐦 . This extends constructions familiar and central in the theory of free Lie algebras, noncommutative symmetric functions and their various applications fields, and allows to interpret 𝐖𝐐𝐒𝐲𝐦 as a convolution algebra of linear endomorphisms of quasi-shuffle...

Non-commutative separability and group actions.

Ricardo Alfaro (1992)

Publicacions Matemàtiques

We give conditions for the skew group ring S * G to be strongly separable and H-separable over the ring S. In particular we show that the H-separability is equivalent to S being central Galois extension. We also look into the H-separability of the ring S over the fixed subring R under a faithful action of a group G. We show that such a chain: S * G H-separable over S and S H-separable over R cannot occur, and that the centralizer of R in S is an Azumaya algebra in the presence of a central element...

On centralizers of semiprime rings

Borut Zalar (1991)

Commentationes Mathematicae Universitatis Carolinae

Let 𝒦 be a semiprime ring and T : 𝒦 → 𝒦 an additive mapping such that T ( x 2 ) = T ( x ) x holds for all x ∈ 𝒦 . Then T is a left centralizer of 𝒦 . It is also proved that Jordan centralizers and centralizers of 𝒦 coincide.

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