My question may seem silly at first, but currently I am not able to work out the question of finding all roots for the n-dimensional torus. At first, it seemed obvious to me that there are no roots at all. However, after trying to prove it I got stuck. Let us consider the 1-dimensional torus ( circle). The roots are simultaneous eigenvalues of the differential operators associated to the basis of maximal cartan subalgebra. What is the Lie algebra of the 1-dim torus at neutral element? Apparently, it is real line. What is multiplication in this algebra and all the stupid questions like that. I am lost in these small silly problems and can't answer the initial question ?
2026-03-25 20:34:41.1774470881
What are the root systems for the n-dimensional torus?
351 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LIE-GROUPS
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