BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Miodrag Iovanov (University of Iowa\, USA) DTSTART:20220308T170000Z DTEND:20220308T180000Z DTSTAMP:20260423T035908Z UID:ONCAS/14 DESCRIPTION:Title: Q uantum groups of finite representation type\nby Miodrag Iovanov (Unive rsity of Iowa\, USA) as part of ONCAS Online Noncommutative Algebra Semina r\n\n\nAbstract\nAlgebras of finite representation type - that is\, those who have only finitely many indecomposable finite dimensional representati ons up to isomorphism - have been of central interest in representation th eory. Classically\, they appeared from work in modular representations\; a (finite) group has finite representation type iff its p-Sylow subgroup is cyclic. On the quantum side\, results of Farnsteiner describe the structu re of finite group schemes (finite dimensional co-commutative Hopf algebra s). Among the first examples of non-commutative and non-cocommutative quan tum groups (Hopf algebras) are the Sweedler algebra and Taft algebras. The se are pointed (their simple modules are 1-dimensional - they are points)\ , and they are also of finite type.\n\nTo study this in the generality of infinite dimensional quantum groups (which includes gl_n\, quantum sl\, et c.)\, one defines an algebra to be of finite type if given any dimension v ector\, there are only finitely many indecomposables of this dimension vec tor\; by the well known Brower-Thrall problems\, this is equivalent to the above for finite dimensional algebras. We give an overview of various exa mples of infinte quantum groups of finite type\, and give a complete class ification of the pointed quantum groups of finite representation type. We re-obtain results known for the finite dimensional case (including Taft al gebras and their generalizations)\, and show that these include several in teresting Hopf algebras\, such as those whose categories of comodules form the category of chain complexes or the category of double chain complexes \, and in general\, the list includes these and certain kind of twists and deformations of theirs.\n LOCATION:https://researchseminars.org/talk/ONCAS/14/ END:VEVENT END:VCALENDAR