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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...

Nonlinearity of the automorphism groups of some free algebras.

Roman'kov, V.A., Chirkov, I.V., Shevelin, M.A. (2004)

Sibirskij Matematicheskij Zhurnal

Notes on Galois extensions with inner Galois groups.

Jiang, X.-L., Szeto, G. (1999)

Portugaliae Mathematica

Displaying 1 – 4 of 4

Natural endomorphisms of quasi-shuffle Hopf algebras

Non-commutative separability and group actions.

Nonlinearity of the automorphism groups of some free algebras.

Notes on Galois extensions with inner Galois groups.

Currently displaying 1 – 4 of 4