Standard

Axial view on pseudo-composition algebras and train algebras of rank 3. / Gorshkov, I.; Mamontov, A.; Staroletov, A.

In: International Journal of Algebra and Computation, Vol. 34, No. 6, 01.09.2024, p. 937-960.

Research output: Contribution to journal › Article › peer-review

Harvard

Gorshkov, I, Mamontov, A & Staroletov, A 2024, 'Axial view on pseudo-composition algebras and train algebras of rank 3', International Journal of Algebra and Computation, vol. 34, no. 6, pp. 937-960. https://doi.org/10.1142/S0218196724500383

APA

Gorshkov, I., Mamontov, A., & Staroletov, A. (2024). Axial view on pseudo-composition algebras and train algebras of rank 3. International Journal of Algebra and Computation, 34(6), 937-960. https://doi.org/10.1142/S0218196724500383

Vancouver

Gorshkov I, Mamontov A, Staroletov A. Axial view on pseudo-composition algebras and train algebras of rank 3. International Journal of Algebra and Computation. 2024 Sep 1;34(6):937-960. https://doi.org/10.1142/S0218196724500383

Author

Gorshkov, I. ; Mamontov, A. ; Staroletov, A. / Axial view on pseudo-composition algebras and train algebras of rank 3. In: International Journal of Algebra and Computation. 2024 ; Vol. 34, No. 6. pp. 937-960.

BibTeX

@article{d5b307a2608649e596a885ca2ddf3870,
title = "Axial view on pseudo-composition algebras and train algebras of rank 3",
abstract = "We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called PC(η)-axial algebras, where η is an element of the ground field. As a first step toward their classification, we describe the 2- and 3-generated subalgebras of such algebras. {\textcopyright} World Scientific Publishing Company.",
keywords = "axial algebra, idempotent, Peirce decomposition, Pseudo-composition algebra, train algebra",
author = "I. Gorshkov and A. Mamontov and A. Staroletov",
note = "Export Date: 19 October 2024 Адрес для корреспонденции: Gorshkov, I.; Sobolev Institute of Mathematics, Russian Federation; эл. почта: ilygor8@gmail.com Сведения о финансировании: Russian Science Foundation, RSF, 22-11-00081 Сведения о финансировании: FWNF-2022-0002 Текст о финансировании 1: We would like to thank Prof. Sergey Shpectorov for useful comments on an earlier draft of this paper. We also thank the referee for helpful comments that improved the quality of this paper. Ilya Gorshkov and Andrey Mamontov are supported by the Russian Scientific Foundation (Project No. 22-11-00081, https://rscf.ru/en/project/22-11-00081/) and Alexey Staroletov is supported by the RAS Fundamental Research Program (Project FWNF-2022-0002).",
year = "2024",
month = sep,
day = "1",
doi = "10.1142/S0218196724500383",
language = "Английский",
volume = "34",
pages = "937--960",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "6",

}

RIS

TY - JOUR

T1 - Axial view on pseudo-composition algebras and train algebras of rank 3

AU - Gorshkov, I.

AU - Mamontov, A.

AU - Staroletov, A.

N1 - Export Date: 19 October 2024 Адрес для корреспонденции: Gorshkov, I.; Sobolev Institute of Mathematics, Russian Federation; эл. почта: ilygor8@gmail.com Сведения о финансировании: Russian Science Foundation, RSF, 22-11-00081 Сведения о финансировании: FWNF-2022-0002 Текст о финансировании 1: We would like to thank Prof. Sergey Shpectorov for useful comments on an earlier draft of this paper. We also thank the referee for helpful comments that improved the quality of this paper. Ilya Gorshkov and Andrey Mamontov are supported by the Russian Scientific Foundation (Project No. 22-11-00081, https://rscf.ru/en/project/22-11-00081/) and Alexey Staroletov is supported by the RAS Fundamental Research Program (Project FWNF-2022-0002).

PY - 2024/9/1

Y1 - 2024/9/1

N2 - We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called PC(η)-axial algebras, where η is an element of the ground field. As a first step toward their classification, we describe the 2- and 3-generated subalgebras of such algebras. © World Scientific Publishing Company.

AB - We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called PC(η)-axial algebras, where η is an element of the ground field. As a first step toward their classification, we describe the 2- and 3-generated subalgebras of such algebras. © World Scientific Publishing Company.

KW - axial algebra

KW - idempotent

KW - Peirce decomposition

KW - Pseudo-composition algebra

KW - train algebra

UR - https://www.mendeley.com/catalogue/200ed256-2ba0-3921-8cff-53b526347bc0/

U2 - 10.1142/S0218196724500383

DO - 10.1142/S0218196724500383

M3 - статья

VL - 34

SP - 937

EP - 960

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 6

ER -

ID: 126390230