Isotopisms of nilpotent Leibniz algebras and Lie racks
In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every nilpotent Leibniz algebra (Formula presented.) with (Formula presented.) is isotopic to the Heisenberg Lie algebra or to the Heisenberg algebra (Formula presented.), where J1 is the n × n Jordan block of...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | COMMUNICATIONS IN ALGEBRA
52 No. 9 |
| Tárgyszavak: | |
| doi: | 10.1080/00927872.2024.2330686 |
| mtmt: | 34785842 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/32942 |
| Tartalmi kivonat: | In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every nilpotent Leibniz algebra (Formula presented.) with (Formula presented.) is isotopic to the Heisenberg Lie algebra or to the Heisenberg algebra (Formula presented.), where J1 is the n × n Jordan block of eigenvalue 1. We also prove that two such algebras are isotopic if and only if the Lie racks integrating them are isotopic. This gives the classification of Lie racks whose tangent space at the unit element is a nilpotent Leibniz algebra with one-dimensional commutator ideal. Eventually, we introduce new isotopism invariants for Leibniz algebras and Lie racks. © 2024 Taylor & Francis Group, LLC. |
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| Terjedelem/Fizikai jellemzők: | 3812-3825 |
| ISSN: | 0092-7872 |