Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation

We consider the algebras eiΠλ (Q)ei , where Πλ (Q) is the deformed preprojective algebra of weight λ and i is some vertex of Q, in the case where Q is an extended Dynkin diagram and λ lies on the hyperplane orthogonal to the minimal positive imaginary root δ. We prove that the center of eiΠλ (...

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Збережено в:
Бібліографічні деталі
Дата:2004
Автор: Mellit, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2004
Назва видання:Algebra and Discrete Mathematics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/156459
Теги: Додати тег
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation / A. Mellit // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 89–110. — Бібліогр.: 5 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме:We consider the algebras eiΠλ (Q)ei , where Πλ (Q) is the deformed preprojective algebra of weight λ and i is some vertex of Q, in the case where Q is an extended Dynkin diagram and λ lies on the hyperplane orthogonal to the minimal positive imaginary root δ. We prove that the center of eiΠλ (Q)ei is isomorphic to Oλ (Q), a deformation of the coordinate ring of the Kleinian singularity that corresponds to Q. We also find a minimal k for which a standard identity of degree k holds in eiΠλ (Q)ei . We prove that the algebras AP₁,...,Pn;µ = Chx₁, . . . , xn|Pi(xi) = 0, Pn i=1 x₁ = µei make a special case of the algebras ecΠλ (Q)ec for star-like quivers Q with the origin c.