Research Article
A∞-algebra Structure on Connected Multiplicative Operad
Batkam Mbatchou Vane Jacky III*,
Calvin Tcheka
Issue:
Volume 13, Issue 5, October 2024
Pages:
72-78
Received:
2 August 2024
Accepted:
9 September 2024
Published:
29 September 2024
DOI:
10.11648/j.pamj.20241305.12
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Abstract: This work develops the structure of A∞-algebras on operad theory and also the preservation of this structure by a morphism of operads well defined. This structure defined here is motivated by the important role that play certain particular properties such as multiplication and connectivity on the operads. Another key ingredient used to develop this work is the brace operations; which, combined with the properties cited above allowed to better frame the study of this structure. Thus, this paper show explicitly the existence of an A∞-algebra structure on any connected multiplicative operad endowed with its brace operations and that this structure is minimal if the operad is only multiplicative. Furthermore, the paper also shows the existence of an operads morphism from an unital associative operad, Ass to any connected multiplicative operad 𝒪 preserving the structure of A∞-algebras existing on these two operads. And when the operad 𝒪 is just multiplicative then there is rather a morphism of operads from the associative operad, Asto 𝒪 preserving this time the minimal A∞-algebras structure existing on these operads.
Abstract: This work develops the structure of A∞-algebras on operad theory and also the preservation of this structure by a morphism of operads well defined. This structure defined here is motivated by the important role that play certain particular properties such as multiplication and connectivity on the operads. Another key ingredient used to develo...
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