2015/12/17 by Wang, Z., Li, L., Zhang, Y.
#16W30 #19A22 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1512.05621
In this paper, we study the Green ring and the stable Green ring of a Hopf algebra H by means of bilinear forms. We show that the Green ring of a Hopf algebra of finite representation type is a Frobenius algebra over ℤ with a dual basis associated to almost split sequences. On the stable Green ring we define a new bilinear form which is more accurate to determine the bi-Frobenius property of the stable Green ring. We show that the complexified stable Green ring (or algebra) is a group-like algebra, and hence a bi-Frobenius algebra, if the bilinear form on the stable Green ring is non-degenerate.