This is a section of the Basic Math Library List

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 7. Lie theory and generalizations
     Algebraic and arithmetic groups. Structure, geometry and representations of Lie groups and Lie algebras. 
     Related geometric and algebraic objects, e.g. symmetric spaces, buildings, vertex operator algebras, quantum groups. 
     Non-commutative harmonic analysis. Geometric methods in representation theory. Discrete subgroups of Lie groups. 
     Lie groups and dynamics, including applications to number theory.
     Connections with sections  2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14.

Lie Groups and Symmetric Spaces

  • Adams, J. Frank. Lectures on Lie Groups Chicago, IL: University of Chicago Press, 1982.
    • Chevalley, Claude. Theory of Lie Groups Princeton, NJ: Princeton University Press, 1946.

Dieudonne, Jean. Special Functions and Linear Representations of Lie Groups Providence, RI: American Mathematical Society, 1980.

Helgason, Sigurdur. Groups and Harmonic Analysis New York, NY: Academic Press, 1984.

  • Helgason, Sigurdur. Differential Geometry, Lie Groups, and Symmetric Spaces New York, NY: Academic Press, 1978.

Montgomery, Deane and Zippin, Leo. Topological Transformation Groups Melbourne, FL: Robert E. Krieger, 1974.

Sugiura, Mitsuo. Unitary Representations and Harmonic Analysis: An Introduction New York, NY: Halsted Press, 1975.

  • Terras, Audrey. Harmonic Analysis on Symmetric Spaces and Applications, New York, NY: Springer-Verlag, 1985, 1988. 2 Vols.

Lie Algebras

Humphreys, James E. Introduction to Lie Algebras and Representation Theory New York, NY: Springer-Verlag, 1972.

  • Jacobson, Nathan. Lie Algebras Mineola, NY: Dover, 1979.
  • Kaplansky, Irving. Lie Algebras and Locally Compact Groups Chicago, IL: University of Chicago Press, 1971.
  • Samelson, Hans. Notes on Lie Algebras New York, NY: Springer-Verlag, 1990.

Winter, David J. Abstract Lie Algebras Cambridge, MA: MIT Press, 1972.

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