Planar trees, free nonassociative algebras, invariants, and elliptic integrals
We consider absolutely free algebras with (maybe infinitely) many multilinear operations. Such multioperator algebras were introduced by Kurosh in 1960. Multioperator algebras satisfy the Nielsen-Schreier property and subalgebras of free algebras are also free. Free multioperator algebras are descri...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2008 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2008
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152390 |
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| Цитувати: | Planar trees, free nonassociative algebras, invariants, and elliptic integrals / V. Drensky, R. Holtkamp // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 1–41. — Бібліогр.: 48 назв. — англ |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152390 |
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dspace |
| spelling |
irk-123456789-1523902019-06-11T01:25:30Z Planar trees, free nonassociative algebras, invariants, and elliptic integrals Drensky, V. Holtkamp, R. We consider absolutely free algebras with (maybe infinitely) many multilinear operations. Such multioperator algebras were introduced by Kurosh in 1960. Multioperator algebras satisfy the Nielsen-Schreier property and subalgebras of free algebras are also free. Free multioperator algebras are described in terms of labeled reduced planar rooted trees. This allows to apply combinatorial techniques to study their Hilbert series and the asymptotics of their coefficients. Then, over a field of characteristic 0, we investigate the subalgebras of invariants under the action of a linear group, their sets of free generators and their Hilbert series. It has turned out that, except in the trivial cases, the algebra of elliptic integrals. invariants is never finitely generated. In important partial cases the Hilbert series of the algebras of invariants and the generating functions of their sets of free generators are expressed in terms of elliptic integrals. 2008 Article Planar trees, free nonassociative algebras, invariants, and elliptic integrals / V. Drensky, R. Holtkamp // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 1–41. — Бібліогр.: 48 назв. — англ 1726-3255 2000 Mathematics Subject Classification:17A50, 17A36, 17A42, 15A72,33E05. http://dspace.nbuv.gov.ua/handle/123456789/152390 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 absolutely free algebras with (maybe infinitely) many multilinear operations. Such multioperator algebras were introduced by Kurosh in 1960. Multioperator algebras satisfy the Nielsen-Schreier property and subalgebras of free algebras are also free. Free multioperator algebras are described in terms of labeled reduced planar rooted trees. This allows to apply combinatorial techniques to study their Hilbert series and the asymptotics of their coefficients. Then, over a field of characteristic 0, we investigate the subalgebras of invariants under the action of a linear group, their sets of free generators and their Hilbert series. It has turned out that, except in the trivial cases, the algebra of elliptic integrals. invariants is never finitely generated. In important partial cases the Hilbert series of the algebras of invariants and the generating functions of their sets of free generators are expressed in terms of elliptic integrals. |
| format |
Article |
| author |
Drensky, V. Holtkamp, R. |
| spellingShingle |
Drensky, V. Holtkamp, R. Planar trees, free nonassociative algebras, invariants, and elliptic integrals Algebra and Discrete Mathematics |
| author_facet |
Drensky, V. Holtkamp, R. |
| author_sort |
Drensky, V. |
| title |
Planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| title_short |
Planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| title_full |
Planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| title_fullStr |
Planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| title_full_unstemmed |
Planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| title_sort |
planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152390 |
| citation_txt |
Planar trees, free nonassociative algebras, invariants, and elliptic integrals / V. Drensky, R. Holtkamp // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 1–41. — Бібліогр.: 48 назв. — англ |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:38:16Z |
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2023-05-20T17:38:16Z |
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