Axial algebras of Monster type (2η,η) for D diagrams. I Full article
| Journal |
Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125 |
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| Output data | Year: 2025, Pages: 1-35 Pages count : 35 DOI: 10.1080/00927872.2025.2457010 | ||
| Tags | Axial algebra; Matsuo algebra; double axis; 3-transpostion group | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
Axial algebras are a class of commutative algebras generated by idempotents with adjoint action semisimple and satisfying a prescribed fusion law. The class of Matsuo algebras was introduced by Matsuo and later generalized by Hall, Rehren, and Shpectorov. A Matsuo algebra M is built by a set of 3-transpositions D. Elements of D are idempotents in M and called axes. It is known that double axes, i.e., sums of two orthogonal axes in a Matsuo algebra, satisfy the fusion law of Monster type. In this paper, we study primitive subalgebras generated by a single axis and two double axes. We classify all such subalgebras in seven out of nine possible cases for a diagram on 3-transpositions that are involved in the generating elements. We also construct several infinite series of axial algebras of Monster type generalizing our 3-generated algebras.
Cite:
Mamontov A.
, Staroletov A.
Axial algebras of Monster type (2η,η) for D diagrams. I
Communications in Algebra. 2025. С.1-35. DOI: 10.1080/00927872.2025.2457010 WOS Scopus OpenAlex
Axial algebras of Monster type (2η,η) for D diagrams. I
Communications in Algebra. 2025. С.1-35. DOI: 10.1080/00927872.2025.2457010 WOS Scopus OpenAlex
Dates:
| Submitted: | Jan 5, 2023 |
| Accepted: | Jan 14, 2025 |
| Published online: | Feb 7, 2025 |
Identifiers:
| Web of science: | WOS:001467505300001 |
| Scopus: | 2-s2.0-85217577188 |
| OpenAlex: | W4407251770 |
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