BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Raphael Bennett-Tennenhaus (Bielefeld University) DTSTART:20220322T140000Z DTEND:20220322T150000Z DTSTAMP:20260423T004756Z UID:TRAC/39 DESCRIPTION:Title: Se milinear clannish algebras\nby Raphael Bennett-Tennenhaus (Bielefeld U niversity) as part of The TRAC Seminar - Théorie de Représentations et s es Applications et Connections\n\n\nAbstract\nAbstract: Indecomposable mod ules over string algebras were classified by Butler and Ringel\, and take exactly one of two forms: string modules\, defined by walks in the quiver\ ; or band modules\, given by cyclic walks together with a representation o f the Laurent polynomial ring. Clannish algebras\, introduced by Crawley- Boevey\, are a generalisation of string algebras – where one specifies a set of special loops\, each bounded by some quadratic polynomial. An anal ogue of Butler and Ringel’s result was given where the class of string ( or band) modules splits into so-called asymmetric and symmetric subclasses . Said symmetry is given by reflecting the walk about a special loop\, and symmetric strings and bands are parameterised using appropriate replaceme nts for the Laurent polynomial ring.\n\nBoth string algebras and clannish algebras were defined over a field\, and the quadratics bounding special l oops were assumed to have distinct roots in this field. This talk will be about ongoing joint work with Bill Crawley-Boevey\, where we generalise th e classification for clannish algebras. For the rings we consider we repla ce this field with a division ring equipped with a set of automorphisms\, indexed by arrows of the quiver\, and we allow irreducible quadratics to b ound the special loops. The resulting notion of a semilinear clannish alge bra recovers a generalisation of string algebras considered by Ringel\, wh ere one allows the map associated to an arrow to be semilinear with respec t to its automorphism.\n LOCATION:https://researchseminars.org/talk/TRAC/39/ END:VEVENT END:VCALENDAR