2016/01/22 by Karin Baur, Baur, Karin, Dusko Bogdanic +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1601.05943
arxiv created 2016/01/22 · arxiv updated 2016/01/25
In this paper we study extensions between Cohen-Macaulay modules for algebras arising in the categorifications of Grassmannian cluster algebras. We prove that rank 1 modules are periodic, and we give explicit formulas for the computation of the period based solely on the rim of the rank 1 module in question. We determine \rm Exti(LI, LJ) for arbitrary rank 1 modules LI and LJ. An explicit combinatorial algorithm is given for computation of \rm Exti(LI, LJ) when i is odd, and for i even, we show that \rm Exti(LI, LJ) is cyclic over the centre, and we give an explicit formula for its computation. At the end of the paper we give a vanishing condition of \rm Exti(LI, LJ) for any i>0.