Conjectures on the ring of commuting matrices
نویسنده
چکیده
Let X = (xij) and Y = (yij) be generic n by n matrices and Z = XY − Y X. Let S = k[x11, . . . , xnn, y11, . . . , ynn], where k is a field, let I be the ideal generated by the entries of Z and let R = S/I . We give a conjecture on the first syzygies of I , show how these can be used to give a conjecture on the canonical module of R. Using this and the Hilbert series of I we give a conjecture on the Betti numbers of I in the 4× 4 case. We also give some guesses on the structure of the resolution in general.
منابع مشابه
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تاریخ انتشار 2005