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On representation schemes and Grassmanians of finite dimensional algebras and a construction of Lusztig

2010
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Mathematical Research Letters
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Let I be a finite set and C{I} be the algebra of functions on I. For a finite dimensional C algebra A with C{I} ⊂ A we show that certain moduli spaces of finite dimsional modules are isomorphic to certain Grassmannian (quot-type) varieties. There is a special case of interest in representation theory. Lusztig defined two varieties related to a quiver and gave a bijection between their C-points, [4, Theorem 2.20]. Savage and Tingley raised the question [7, Remark 4.5] of whether these varieties

doi:10.4310/mrl.2010.v17.n5.a13
fatcat:kz5pz7j2gbgl5c7cb3f3dlsugq