The representation theory of non-commutative O(GL2)

In our companion paper "The Manin Hopf algebra of a Koszul Artin–Schelter regular algebra is quasi-hereditary" we used the Tannaka–Krein formalism to study the universal coacting Hopf algebra aut(A) for a Koszul Artin–Schelter regular algebra A. In this paper we study in detail the case A=k[x,y]. In particular we give a more precise description of the standard and costandard representations of aut(A) as a coalgebra and we show that the latter can be obtained by induction from a Borel quotient algebra. Finally we give a combinatorial characterization of the simple aut(A)-representations as tensor products of end(A)-representations and their duals.

Jaar van publicatie:2017

BOF-keylabel:ja

CSS-citation score:1

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Closed