A connected algebraic group Gis called a chainif the lattice of connected algebraic subgroups of Gis a chain, that is: for any two connected algebraic subgroups K,Hof Gwe have either H ≤ Kor K ≤ H. If Gis affine, then Gis a chain if and only if it has a unique connected algebraic subgroup of dimension d, for any d= 1, …, n, because Gis, together with a Borel subgroup of G, nilpotent.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Chains. In: Algebraic Groups and Lie Groups with Few Factors. Lecture Notes in Mathematics, vol 1944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78584-2_4
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DOI: https://doi.org/10.1007/978-3-540-78584-2_4
Publisher Name: Springer, Berlin, Heidelberg
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