<i>A<sub>∞</sub></i>-algebra Structure on Connected Multiplicative Operad

Batkam Mbatchou Vane Jacky III; Calvin Tcheka

doi:doi:10.11648/j.pamj.20241305.12

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A_∞-algebra Structure on Connected Multiplicative Operad

Batkam Mbatchou Vane Jacky III^*, Calvin Tcheka

Published in Pure and Applied Mathematics Journal (Volume 13, Issue 5)

Received: 2 August 2024 Accepted: 9 September 2024 Published: 29 September 2024

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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, A_ss 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.

Published in	Pure and Applied Mathematics Journal (Volume 13, Issue 5)
DOI	10.11648/j.pamj.20241305.12
Page(s)	72-78
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

A_∞-algebra Structure, Minimal A_∞-algebra Structure, Connected Multiplicative Operad, Brace Operations

References

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[3]	Batkam Mbatchou V. JackyIII, Calvin Tcheka, Simplicial Structure on Connected Multiplicative Operads (Arxiv).
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APA Style

III, B. M. V. J., Tcheka, C. (2024). A∞-algebra Structure on Connected Multiplicative Operad. Pure and Applied Mathematics Journal, 13(5), 72-78. https://doi.org/10.11648/j.pamj.20241305.12

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ACS Style

III, B. M. V. J.; Tcheka, C. A∞-algebra Structure on Connected Multiplicative Operad. Pure Appl. Math. J. 2024, 13(5), 72-78. doi: 10.11648/j.pamj.20241305.12

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AMA Style

III BMVJ, Tcheka C. A∞-algebra Structure on Connected Multiplicative Operad. Pure Appl Math J. 2024;13(5):72-78. doi: 10.11648/j.pamj.20241305.12

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@article{10.11648/j.pamj.20241305.12,
  author = {Batkam Mbatchou Vane Jacky III and Calvin Tcheka},
  title = {A∞-algebra Structure on Connected Multiplicative Operad},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {5},
  pages = {72-78},
  doi = {10.11648/j.pamj.20241305.12},
  url = {https://doi.org/10.11648/j.pamj.20241305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241305.12},
  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.},
 year = {2024}
}

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TY  - JOUR
T1  - A∞-algebra Structure on Connected Multiplicative Operad
AU  - Batkam Mbatchou Vane Jacky III
AU  - Calvin Tcheka
Y1  - 2024/09/29
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241305.12
DO  - 10.11648/j.pamj.20241305.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.pamj.20241305.12
AB  - 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.
VL  - 13
IS  - 5
ER  -

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Author Information

Batkam Mbatchou Vane Jacky III

Department of Mathematics, University of Dschang, Dschang, Cameroon

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Calvin Tcheka

Department of Mathematics, University of Dschang, Dschang, Cameroon

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APA Style

III, B. M. V. J., Tcheka, C. (2024). A∞-algebra Structure on Connected Multiplicative Operad. Pure and Applied Mathematics Journal, 13(5), 72-78. https://doi.org/10.11648/j.pamj.20241305.12

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ACS Style

III, B. M. V. J.; Tcheka, C. A∞-algebra Structure on Connected Multiplicative Operad. Pure Appl. Math. J. 2024, 13(5), 72-78. doi: 10.11648/j.pamj.20241305.12

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AMA Style

III BMVJ, Tcheka C. A∞-algebra Structure on Connected Multiplicative Operad. Pure Appl Math J. 2024;13(5):72-78. doi: 10.11648/j.pamj.20241305.12

Copy | Download

@article{10.11648/j.pamj.20241305.12,
  author = {Batkam Mbatchou Vane Jacky III and Calvin Tcheka},
  title = {A∞-algebra Structure on Connected Multiplicative Operad},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {5},
  pages = {72-78},
  doi = {10.11648/j.pamj.20241305.12},
  url = {https://doi.org/10.11648/j.pamj.20241305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241305.12},
  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.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - A∞-algebra Structure on Connected Multiplicative Operad
AU  - Batkam Mbatchou Vane Jacky III
AU  - Calvin Tcheka
Y1  - 2024/09/29
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241305.12
DO  - 10.11648/j.pamj.20241305.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 72
EP  - 78
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241305.12
AB  - 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.
VL  - 13
IS  - 5
ER  -

Copy | Download