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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2008 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2008
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152390 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862663431972192256 |
|---|---|
| author | Drensky, V. Holtkamp, R. |
| author_facet | Drensky, V. Holtkamp, R. |
| 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 |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T15:11:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152390 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:11:52Z |
| publishDate | 2008 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Drensky, V. Holtkamp, R. 2019-06-10T18:55:59Z 2019-06-10T18:55:59Z 2008 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. https://nasplib.isofts.kiev.ua/handle/123456789/152390 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. The work of the first author was partially supported by Grant MI-1503/2005 ofthe Bulgarian National Science Fund. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Planar trees, free nonassociative algebras, invariants, and elliptic integrals Article published earlier |
| spellingShingle | Planar trees, free nonassociative algebras, invariants, and elliptic integrals Drensky, V. Holtkamp, R. |
| title | 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_short | Planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| title_sort | planar trees, free nonassociative algebras, invariants, and elliptic integrals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152390 |
| work_keys_str_mv | AT drenskyv planartreesfreenonassociativealgebrasinvariantsandellipticintegrals AT holtkampr planartreesfreenonassociativealgebrasinvariantsandellipticintegrals |