The Moduli Space of 2-step Nilpotent Lie Algebras of Type (p,q)
نویسنده
چکیده
classes in N(p,q). We show that X(p,q) with the quotient topology is homeomorphic to the compact, connected quotient space G(p, so(q,Â)) / SL(q,Â), where SL(q,Â) acts on so(q,Â) and the associated Grassmann manifold G(p, so(q,Â)) by g(Z) = gZgt for Z ∈ so(q,Â) and g ∈ SL(q,Â). It follows immediately that X(p,q) is homeomorphic to X(D−p,q), where D = dim so(q,Â) = (1/2)q(q−1) (duality). For each (p,q) we compute the dimension of X(p,q) = G(p, so(q,Â)) / SL(q,Â), which is defined to be the minimum codimension of an SL(q,Â) orbit in G(p, so(q,Â)).
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