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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| Дата: | 2004 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156459 |
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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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irk-123456789-1564592019-06-19T01:28:35Z Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation Mellit, A. 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. 2004 Article 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. 1726-3255 http://dspace.nbuv.gov.ua/handle/123456789/156459 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Mellit, A. |
| spellingShingle |
Mellit, A. Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation Algebra and Discrete Mathematics |
| author_facet |
Mellit, A. |
| author_sort |
Mellit, A. |
| title |
Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation |
| title_short |
Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation |
| title_full |
Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation |
| title_fullStr |
Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation |
| title_full_unstemmed |
Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation |
| title_sort |
kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156459 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT mellita kleiniansingularitiesandalgebrasgeneratedbyelementsthathavegivenspectraandsatisfyascalarsumrelation |
| first_indexed |
2023-05-20T17:49:37Z |
| last_indexed |
2023-05-20T17:49:37Z |
| _version_ |
1796154189230899200 |