George Benham Seligman, (born 30 April 1927, Attica, New York) is an American mathematician, who works on Lie algebras, especially semi-simple Lie algebras.
Seligman received his bachelor's degree in 1950 from the University of Rochester and his PhD in 1954 from Yale University under Nathan Jacobson with thesis Lie algebras of prime characteristic. After he received his PhD he was a Henry Burchard Fine Instructor at Princeton University from 1954–1956. In 1956 he became an instructor and from 1965 a full professor at Yale, where he was chair of the mathematics department from 1974 to 1977.
For the academic year 1958/59 he was a Fulbright Lecturer at the University of Münster. His doctoral students include James E. Humphreys, Daniel K. Nakano and Robert Lee Wilson.
Since 1959 he has been married to Irene Schwieder and the couple has two daughters.
On Lie algebras of prime characteristic, American Mathematical Society, 1956Liesche Algebren, Schriftenreihe des Mathematischen Instituts der Universität Münster, 1959Modular Lie Algebras, Springer Verlag 1967Rational methods in Lie algebras, Marcel Dekker 1976Rational constructions of modules for simple Lie algebras, American Mathematical Society 1981Construction of Lie Algebras and their Modules, Springer Verlag 1988Articles
"On a class of semisimple restricted Lie algebras". Proc Natl Acad Sci U S A. 40 (8): 726–728. 1954. PMC 534151 . PMID 16589548. doi:10.1073/pnas.40.8.726. "Characteristic ideals and the structure of Lie algebras". Proc. Amer. Math. Soc. 8: 159–164. 1957. MR 0082974. doi:10.1090/s0002-9939-1957-0082974-9. "On automorphisms of Lie algebras of classical type". Trans. Amer. Math. Soc. 92: 430–448. 1959. MR 0106965. doi:10.1090/s0002-9947-1959-0106965-0. "On automorphisms of Lie algebras of classical type. II.". Trans. Amer. Math. Soc. 94: 452–482. 1960. MR 0113969. doi:10.1090/s0002-9947-1960-0113969-9. "On automorphisms of Lie algebras of classical type. III.". Trans. Amer. Math. Soc. 97: 286–312. 1960. MR 0123644. doi:10.1090/s0002-9947-1960-0123644-2. "Some results on Lie p-algebras". Bull. Amer. Math. Soc. 73: 528–530. 1967. MR 0219585. doi:10.1090/s0002-9904-1967-11731-2. "Algebraic Lie groups". Bull. Amer. Math. Soc. 74: 1051–1065. 1968. MR 0232810. doi:10.1090/s0002-9904-1968-12046-4. "On idempotents in reduced enveloping algebras". Trans. Amer. Math. Soc. 355: 3291–3300. 2003. MR 1974688. doi:10.1090/s0002-9947-03-03314-2. 