# Ernest Vinberg

**Ernest Borisovich Vinberg** (Russian: Эрнест Борисович Винберг; born 26 July 1937) is a Russian mathematician, who works on discrete subgroups of Lie groups and representation theory. He introduced Vinberg's algorithm and the Koecher–Vinberg theorem.

He is a recipient of the Humboldt Prize. He is on the executive committee of the Moscow Mathematical Society. In 1983 he was an Invited Speaker with a talk on *Discrete reflection groups in Lobachevsky spaces* at the International Congress of Mathematicians in Warsaw. In 2010 he was elected a member of the American Academy of Arts and Sciences.

His doctoral students include Victor Kac and Boris Weisfeiler.

## Selected publications

*Linear representations of groups*. Birkhäuser, 1989[1]*A Course in Algebra*. American Mathematical Society (AMS), 2003- editor and co-author:
*Lie groups and invariant theory*. AMS, 2005 (contains*Construction of the exceptional simple Lie algebras*) - with A. L. Onishchik:
*Lie groups and algebraic groups*. Springer, 1990; 2012 pbk edition - with V.V. Gorbatsevich, A.L. Onishchik:
*Foundations of Lie groups and Lie transformation groups*. Springer, 1997 *Hyperbolic reflection groups*. Russian Mathematical Surveys, no. 40, 1985, pp. 31–75- (ed.)
*Geometry II*. Encyclopedia of Mathematical Sciences, Springer 1991, (contains : Vinberg et alia:*Geometry of spaces of constant curvature*,*Discrete groups of motions of spaces of constant curvature*)

## References

- Berg, Michael (21 February 2011). "Review of
*Linear Representations of Groups*by Ernest B. Vinberg".*MAA Reviews, Mathematical Association of America*.

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