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Local and 2-local derivations on Lie matrix rings over commutative involutive rings

Authors :
Ayupov, Shavkat
Arzikulov, Farhodjon
Umrzaqov, Sardorbek
Publication Year :
2022

Abstract

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.<br />Comment: 21 pages. arXiv admin note: text overlap with arXiv:2108.03993, arXiv:1803.06281

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2204.03234
Document Type :
Working Paper