Co Algebras Shifts and a theorem by E Abe and M P Schutzenberger

Matthieu Deneufchatel

Description

(Co)-Algebras, Shifts and a theorem by E. Abe and M. P. Schutzenberger Matthieu Deneufchatel Laboratoire d'Informatique de Paris Nord, Universite Paris 13 CIP, 26 October 2010

• then both families


• argument allows


• argument also applies


• vector spaces


• ?f ?


• then there exists


• k? ?

Sujets

• Vector space
• multiplication

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 15
• Langue: English

Extrait

adna (Co)-Algebras,Shifts theorembyE.AbeandM.P.Schu¨tzenberger MatthieuDeneufchaˆtel Laboratoired’InformatiquedeParisNord, Universite´Paris13 ,PIC 26October2010

Notations Inthistalk, .MD nIrtoudtcoin Let(A,µ,u)and(C,Δ,)denoterespectivelyanassociativealgebra withunituandacoalgebra(coassociativewithcounit),kthe groundfield. A ∗ denotesthealgebraicdualofthevectorspaceA. ForV,Wtwovectorspaces,f ∈ Hom(V,W)andv ∈ V, h f | v i denotesthevalueoff(v). Transposeofalinearmap:wedenoteby t f:W ∗ → V ∗ the transposeoff: eenfuhctaˆleL(PIN-1P)3 h t f(w) | v i = h w | f(v) i , ∀ v ∈ V. hSfistnadlAegrbsa621//002012/12