2022/04/07 by Shavkat Ayupov, Ayupov, Shavkat, Farhodjon Arzikulov +3
Mathematics · #17B40 #17B65 #46K70 #46L57 #46L70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2204.03234
openalex publication_date 2022/04/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In the present paper we prove that every 2-local inner derivation on the Lie ring of skew-adjoint matrices over a commutative *-ring is an inner derivation. We also apply our technique to various Lie algebras of infinite-dimensional skew-adjoint matrix-valued maps on a set and prove that every 2-local spatial derivation on such algebras is a spatial derivation. We also show that every local spatial derivation on the above Lie algebras is a derivation.