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Quasi-split group
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<h2 id="examples">Examples</h2> <p>All split groups (those with a split maximal torus) are quasi-split. These correspond to quasi-split groups where the action of the Galois group on the Dynkin diagram is trivial. </p><p>Lang (1956) showed that all simple algebraic groups over finite fields are quasi-split. </p><p>Over the real numbers, the quasi-split groups include the split groups and the complex groups, together with the orthogonal groups <i>O</i><i>n</i>,<i>n</i>+2, the unitary groups <i>SU</i><i>n</i>,<i>n</i> and <i>SU</i><i>n</i>,<i>n</i>+1, and the form of <i>E</i>6 with signature 2. </p> <ul><li><a href="/facts/Serge_Lang/I7MW2rUu">Lang, Serge</a> (1956), "Algebraic groups over finite fields", <i><a href="/facts/American_Journal_of_Mathematics/lkgftcD7">American Journal of Mathematics</a></i>, 78: 555–563, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.2307%2F2372673">10.2307/2372673</a>, <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0002-9327">0002-9327</a>, <a href="/facts/JSTOR_(identifier)/YTeVmaJ7">JSTOR</a> <a href="https://www.jstor.org/stable/2372673">2372673</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0086367">0086367</a></li></ul>