Matrix representation of Lie algebras over rings

V. A. Churkin

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR

Abstract: Over the principal ideal ring $k$, the Lie $k$-algebras which are free $k$-modules of finite rank are, to within isomorphism, the Lie subalgebras of the full matrix algebra $M(n, k)$.

UDC: 512

Received: 10.06.1970

 English version: Mathematical Notes, 1871, 10:6, 835–839

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