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 roo...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2004 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
|
| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734527131025408 |
|---|---|
| author | Mellit, A. |
| author_facet | Mellit, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T19:43:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156459 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:43:43Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Mellit, A. 2019-06-18T14:13:00Z 2019-06-18T14:13:00Z 2004 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 https://nasplib.isofts.kiev.ua/handle/123456789/156459 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation Article published earlier |
| spellingShingle | Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation Mellit, A. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156459 |
| work_keys_str_mv | AT mellita kleiniansingularitiesandalgebrasgeneratedbyelementsthathavegivenspectraandsatisfyascalarsumrelation |