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...
Збережено в:
| 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/123456789/156457 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862682504110014464 |
|---|---|
| author | Bondarenko, V.M. |
| author_facet | Bondarenko, V.M. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T15:52:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156457 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:52:48Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bondarenko, V.M. 2019-06-18T14:12:06Z 2019-06-18T14:12:06Z 2004 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. https://nasplib.isofts.kiev.ua/handle/123456789/156457 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On wildness of idempotent generated algebras associated with extended Dynkin diagrams Article published earlier |
| spellingShingle | On wildness of idempotent generated algebras associated with extended Dynkin diagrams Bondarenko, V.M. |
| title | 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_short | On wildness of idempotent generated algebras associated with extended Dynkin diagrams |
| title_sort | on wildness of idempotent generated algebras associated with extended dynkin diagrams |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156457 |
| work_keys_str_mv | AT bondarenkovm onwildnessofidempotentgeneratedalgebrasassociatedwithextendeddynkindiagrams |