Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Semi-invariant of a quiver the coefficients of the characteristic polynomial In case Q has neither loops nor cycles the variety "k"[Rep(Q,d)] has a unique closed orbit corresponding to the unique d-dimensional semi-simple representation, therefore any invariant function is constant. Elements which are invariants with respect to the subgroup SL(d) := ∏ SL(d("i")) form a ring, SI(Q,d), with a richer structure called ring of semi-invariants. It decomposes as where A function belonging to SI(Q,d) is called semi-invariant of weight "σ". Consider the quiver Q: Fix d = ("n","n"). In this case "k"[Rep("Q",("n","n"))] is congruent to the set of square matrices of size "n": "M"("n"). The