2015/09/13 by Theo Raedschelders, Michel Van den Bergh, Raedschelders, Theo +1
Mathematics · #16S10 #16S37 #16S38 #16T05 #16T15 #20G42 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:16S10 #msc:16S37 #msc:16S38 #msc:16T05 #msc:16T15 #msc:20G42
paper · pdf · doi:10.48550/arxiv.1509.03869
36 pages
arxiv created 2015/09/13 · arxiv updated 2015/09/15
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.