Izvorni znanstveni članak
https://doi.org/10.64785/mc.30.2.3
Uniqueness of addition in Lie algebras revisited
Ivan Arzhantsev
; Faculty of Computer Science, HSE University, Moscow, Russia
*
* Dopisni autor.
Sažetak
We obtain new and improve old results on the uniqueness of addition in Lie rings and Lie algebras. A Lie ring ℜ is called a unique addition Lie ring, or a UA-Lie ring, if any commutator-preserving bijection from ℜ to an arbitrary Lie ring is additive. We describe wide classes of Lie rings that are not UA-Lie rings. On the other hand, it is known that if a finite-dimensional Lie algebra 𝔤 contains two elements whose centralizers have trivial intersection, then 𝔤 is a UA-Lie ring. We use this result to characterize UA-Lie rings among seaweed Lie algebras. The paper includes many open problems and questions.
Ključne riječi
Lie ring; centralizer; semisimple Lie algebra; seaweed subalgebra; radical
Hrčak ID:
335663
URI
Datum izdavanja:
22.9.2025.
Posjeta: 404 *