On wildness of idempotent generated algebras associated with extended Dynkin diagrams
Let Λ denote an extended Dynkin diagram with vertex set Λ0 = {0, 1,... ,n}. For a vertex i, denote by S(i) the set of vertices j such that there is an edge joining i and j; one assumes the diagram has a unique vertex p, say p = 0, with |S(p)| = 3. Further, denote by Λ \ 0 the full subgraph of Λ...
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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/123456789/156457 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On wildness of idempotent generated algebras associated with extended Dynkin diagrams / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 1–11. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156457 |
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irk-123456789-1564572019-06-19T01:27:48Z On wildness of idempotent generated algebras associated with extended Dynkin diagrams Bondarenko, V.M. Let Λ denote an extended Dynkin diagram with vertex set Λ0 = {0, 1,... ,n}. For a vertex i, denote by S(i) the set of vertices j such that there is an edge joining i and j; one assumes the diagram has a unique vertex p, say p = 0, with |S(p)| = 3. Further, denote by Λ \ 0 the full subgraph of Λ with vertex set Λ0 \ {0}. Let ∆ = (δi |i ∈ Λ0) ∈ Z |Λ0| be an imaginary root of Λ, and let k be a field of arbitrary characteristic (with unit element 1). We prove that if Λ is an extended Dynkin diagram of type D₄, E₆ or E₇, then the k-algebra Qk(Λ, ∆) with generators ei , i ∈ Λ0 \ {0}, and relations e 2 i = ei , eiej = 0 if i and j 6= i belong to the same connected component of Λ \ 0, and Pn i=1 δi ei = δ01 has wild representation time. 2004 Article On wildness of idempotent generated algebras associated with extended Dynkin diagrams / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 1–11. — Бібліогр.: 4 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 16G60; 15A21, 46K10, 46L05. http://dspace.nbuv.gov.ua/handle/123456789/156457 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 |
Let Λ denote an extended Dynkin diagram with
vertex set Λ0 = {0, 1,... ,n}. For a vertex i, denote by S(i) the set
of vertices j such that there is an edge joining i and j; one assumes
the diagram has a unique vertex p, say p = 0, with |S(p)| = 3.
Further, denote by Λ \ 0 the full subgraph of Λ with vertex set
Λ0 \ {0}. Let ∆ = (δi
|i ∈ Λ0) ∈ Z
|Λ0| be an imaginary root of Λ,
and let k be a field of arbitrary characteristic (with unit element
1). We prove that if Λ is an extended Dynkin diagram of type
D₄, E₆ or E₇, then the k-algebra Qk(Λ, ∆) with generators ei
,
i ∈ Λ0 \ {0}, and relations e
2
i = ei
, eiej = 0 if i and j 6= i belong to
the same connected component of Λ \ 0, and Pn
i=1 δi ei = δ01 has
wild representation time. |
| format |
Article |
| author |
Bondarenko, V.M. |
| spellingShingle |
Bondarenko, V.M. On wildness of idempotent generated algebras associated with extended Dynkin diagrams Algebra and Discrete Mathematics |
| author_facet |
Bondarenko, V.M. |
| author_sort |
Bondarenko, V.M. |
| title |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams |
| title_short |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams |
| title_full |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams |
| title_fullStr |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams |
| title_full_unstemmed |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams |
| title_sort |
on wildness of idempotent generated algebras associated with extended dynkin diagrams |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156457 |
| citation_txt |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 1–11. — Бібліогр.: 4 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT bondarenkovm onwildnessofidempotentgeneratedalgebrasassociatedwithextendeddynkindiagrams |
| first_indexed |
2023-05-20T17:49:36Z |
| last_indexed |
2023-05-20T17:49:36Z |
| _version_ |
1796154189022232576 |