On observable module categories

NICOLÁS ANDRUSKIEWITSCH; WALTER FERRER SANTOS

Groups, Rings and Group Rings

Chapman \& Hall/CRC

Lugar: Boca Raton, FL; Año: 2006; p. 11 - 23

The purpose of the present paper is to begin the study of a class of module categoriesover a tensor category C that we call observable module categories. These module categoriesare simple in a suitable sense (that we introduce in this paper). If C = GM then thearchetypical example is the module category of H-modules,  where H is an observable subgroup of G. We extend some well-known results on observable subgroups to the setting of quotients of Hopf algebras.The notion of observable subgroup has the following geometric characterization: a closedsubgroup H of an algebraic group G is observable iff the homogeneous space G/H is quasi-affine. This suggests that the study of observable module categories could have a "non-commutative geometry" flavor: they should correspond to "non-commutative quasi-affinevarieties".