On wildness of idempotent generated algebras associated with extended Dynkin diagrams
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On wildness of idempotent generated algebras associated with extended Dynkin diagrams
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| Creator |
Bondarenko, V.M.
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| 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. |
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| Date |
2019-06-18T14:12:06Z
2019-06-18T14:12:06Z 2004 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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