Details

Autor(en) / Beteiligte

• ETINGOF, PAVEL
• WALTON, CHELSEA

Titel

POINTED HOPF ACTIONS ON FIELDS, I

Ist Teil von

• Transformation groups, 2015-12, Vol.20 (4), p.985-1013

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2015

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic zero on commutative domains were classified recently by the authors in [18]. The answer turns out to be very simple–if the action is inner faithful, then H has to be a group algebra. The present article contributes to the non-semisimple case, which is much more complicated. Namely, we study actions of finite dimensional (not necessarily semisimple) Hopf algebras on commutative domains, particularly when H is pointed of finite Cartan type. The work begins by reducing to the case where H acts inner faithfully on a field; such a Hopf algebra is referred to as Galois-theoretical. We present examples of such Hopf algebras, which include the Taft algebras, uq( s l 2 ), and some Drinfeld twists of other small quantum groups. We also give many examples of finite dimensional Hopf algebras which are not Galois-theoretical. Classification results on finite dimensional pointed Galois-theoretical Hopf algebras of finite Cartan type will be provided in the sequel, Part II, of this study.