Séminaires et Congrès - 2 - pages 137-148 < Séminaires et Congrès < 2

Algèbre non commutative, groupes quantiques et invariants Septième contact Franco-Belge, Reims, Juin 1995
J. Alev, G. Cauchon (Éd.)
Séminaires et Congrès 2 (1997), 304 pages

Quantum Serre Relations
Claus Michael RINGEL
Séminaires et Congrès 2 (1997), 137-148
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Résumé :
Let ${\Bbb Z}I$ be the free abelian group with basis I, let $\chi$ be a pair of integral bilinear forms on ${\Bbb Z}I$. We will endow the free K-algebra $K\langle I\rangle$ generated by I with a comultiplication which depends on $\chi$. This yields an associated bilinear form on $K\langle I\rangle$ which may be called the Drinfeld form. We are going to show that certain elements of $K\langle I\rangle$ which are similar to the well-known quantum Serre relations belong to the left radical of the Drinfeld form, provided certain integrality conditions are satisfied.

Class. math. : 16W30, 17B37

ISBN : 2-85629-052-3
Publié avec le concours de : Centre National de la Recherche Scientifique