Seligman was born on April 30, 1927.^[1] He 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.^[2] 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, Brian J Parshall, and Daniel K. Nakano.

Seligman married Irene Schwieder in 1959. The couple had two daughters. He died in Hamden, Connecticut, on April 25, 2024, at the age of 96.^[3]

• On Lie algebras of prime characteristic, American Mathematical Society, 1956
• Liesche Algebren, Schriftenreihe des Mathematischen Instituts der Universität Münster, 1959
• Modular Lie Algebras, Springer Verlag 1967^[4]
• Rational methods in Lie algebras, Marcel Dekker 1976^[5]
• Rational constructions of modules for simple Lie algebras, American Mathematical Society 1981
• Construction of Lie Algebras and their Modules, Springer Verlag 1988

• Seligman, G. B. (1954). "On a class of semisimple restricted Lie algebras". Proceedings of the National Academy of Sciences of the United States of America. 40 (8): 726–728. Bibcode:1954PNAS...40..726S. doi:10.1073/pnas.40.8.726. PMC 534151. PMID 16589548.
• Seligman, George B. (1957). "Characteristic ideals and the structure of Lie algebras". Proceedings of the American Mathematical Society. 8: 159–164. doi:10.1090/s0002-9939-1957-0082974-9. MR 0082974.
• Seligman, George B. (1959). "On automorphisms of Lie algebras of classical type". Transactions of the American Mathematical Society. 92 (3): 430–448. doi:10.1090/s0002-9947-1959-0106965-0. MR 0106965.
• Seligman, George B. (1960). "On automorphisms of Lie algebras of classical type. II". Trans. Amer. Math. Soc. 94 (3): 452–482. doi:10.1090/s0002-9947-1960-0113969-9. MR 0113969.
• Seligman, George B. (1960). "On automorphisms of Lie algebras of classical type. III". Trans. Amer. Math. Soc. 97 (2): 286–312. doi:10.1090/s0002-9947-1960-0123644-2. MR 0123644.
• Seligman, George B. (1967). "Some results on Lie p-algebras". Bulletin of the American Mathematical Society. 73 (4): 528–530. doi:10.1090/s0002-9904-1967-11731-2. MR 0219585.
• "Algebraic Lie groups". Bull. Amer. Math. Soc. 74: 1051–1065. 1968. doi:10.1090/s0002-9904-1968-12046-4. MR 0232810.
• Seligman, George B. (2003). "On idempotents in reduced enveloping algebras". Trans. Amer. Math. Soc. 355 (8): 3291–3300. doi:10.1090/s0002-9947-03-03314-2. MR 1974688.