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Licensed Unlicensed Requires Authentication Published by De Gruyter May 21, 2015

A note on real algebraic groups

Hassan Azad and Indranil Biswas
From the journal Forum Mathematicum


The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular, the following two results are proved: (i) Let G be a connected solvable linear group whose eigenvalues are all real. If the complexification G of G is algebraic and operates algebraically on a complex variety V, and some G orbit in V is compact, then this orbit is a point. (ii) If L is a connected subgroup of a connected real linear semisimple group G such that the complexification L of L is algebraic and L contains a maximal torus of G, then L contains a maximal torus of G which complexifies to a maximal torus of G.

Funding source: KFUPM

Award Identifier / Grant number: IN131058

Funding statement: The first author thanks KFUPM for funding Research Project IN131058. The second author acknowledges the support of the J. C. Bose Fellowship.

Received: 2014-8-25
Published Online: 2015-5-21
Published in Print: 2016-5-1

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