Primitive axial algebras are of Jordan type |
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| Affiliation: | 1. Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel;2. Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel;1. University of Missouri-Columbia, Mathematics Department, Columbia, MO, USA;2. College of the Ozarks, Mathematics Department, Point Lookout, MO, USA;1. Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;2. Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;1. Università degli Studi di Udine, Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Via delle Scienze 206, 33100 Udine, Italy;2. Università degli Studi di Firenze, Dipartimento di Matematica e Informatica, Viale Morgagni, 67/a, 50134 Firenze, Italy;3. Institut de Mathématiques, Université de Neuchâtel, Emile-Argand 11, CH-2000 Neuchâtel, Switzerland |
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| Abstract: | The notion of axial algebra is closely related to 3-transposition groups, the Monster group and vertex operator algebras. In this work we continue our previous works and complete the proof that all algebras generated by a set of primitive axes not necessarily of the same type (see the definition in the body of the paper), are primitive axial algebras of Jordan type. |
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| Keywords: | Axis Axial algebra Fusion Idempotent |
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