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Algebra and Discrete Mathematics, 2008, выпуск 2, страницы 1–41
(Mi adm156)
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Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)
RESEARCH ARTICLE
Planar trees, free nonassociative algebras, invariants, and elliptic integrals
Vesselin Drenskya, Ralf Holtkampb a Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences, 1113 Sofia,
Bulgaria
b Fakultät für Mathematik, Ruhr-Universität,
44780 Bochum, Germany
Аннотация:
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 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.
Поступила в редакцию: 03.01.2008 Исправленный вариант: 15.07.2008
Образец цитирования:
Vesselin Drensky, Ralf Holtkamp, “Planar trees, free nonassociative algebras, invariants, and elliptic integrals”, Algebra Discrete Math., 2008, no. 2, 1–41
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm156 https://www.mathnet.ru/rus/adm/y2008/i2/p1
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Страница аннотации: | 244 | PDF полного текста: | 92 | Первая страница: | 1 |
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