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Quasiderivations in diagonal matrix algebras. (English) Zbl 0832.16031
Bokut’, L. A. (ed.) et al., Third Siberian school on algebra and analysis. Proceedings of the third Siberian school, Irkutsk State University, Irkutsk, Russia, August 30-September 4, 1989. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 163, 1-5 (1995).
Let $$A$$ be the algebra of all diagonal matrices over a field of characteristic 0. The author shows that 0 is the only quasiderivation of $$A$$, and thereby answers a question of Eh. B. Vinberg.
For the entire collection see [Zbl 0816.00016].
##### MSC:
 16W25 Derivations, actions of Lie algebras 16S50 Endomorphism rings; matrix rings
##### Keywords:
algebra of diagonal matrices; quasiderivations