Description of 2-local derivations and automorphisms on finite-dimensional Jordan algebras
Shavkat AyupovDepartment of Algebra and Functional Analysis, National University of Uzbekistan, Tashkent, UzbekistanFarhodjon ArzikulovDepartment of Mathematics, Andizhan State University, Andizhan, UzbekistanNodirbek UmrzaqovDepartment of Mathematics, Andizhan State University, Andizhan, UzbekistanOlimjon NuriddinovDepartment of Mathematics, Andizhan State University, Andizhan, Uzbekistan
ABI
Аннотация
In the present paper, we introduce and investigate the notion of 2-local linear maps on vector spaces. A sufficient condition is obtained for the linearity of a 2-local linear map on finite-dimensional vector spaces. Based on this result, we prove that every 2-local derivation on a finite-dimensional semisimple Jordan algebra over an algebraically closed field of characteristic different from 2 is a derivation. Also, we show that every 2-local 1-automorphism (i.e. implemented by single symmetries) of mentioned Jordan algebra is an automorphism.
Мавзулар
Идентификаторлар
Иқтибослар ва манбалар
0 та иқтибос12 та фойдаланилган манба
Кўрсаткичлар — AkademScholar · Тез орада