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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
Dendriform Algebras Relative to a Semigroup
Marcelo Aguiar Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
Аннотация:
Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual operation is replaced by a family of operations indexed by a fixed semigroup $S$. The purpose of this note is twofold. First, we add to the existing work by showing that a similar extension is possible already for the most familiar types of algebra: commutative, associative, and Lie. Second, we show that these concepts arise naturally and in a unified manner from a categorical perspective. For this, one simply has to consider the standard types of algebra but in reference to the monoidal category of $S$-graded vector spaces.
Ключевые слова:
dendriform algebra, monoidal category, dimonoidal category.
Поступила: 9 апреля 2020 г.; в окончательном варианте 29 июня 2020 г.; опубликована 11 июля 2020 г.
Образец цитирования:
Marcelo Aguiar, “Dendriform Algebras Relative to a Semigroup”, SIGMA, 16 (2020), 066, 15 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1603 https://www.mathnet.ru/rus/sigma/v16/p66
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