Lie superalgebras

September 18 - September 29

Institut Henri Poincare

Michel Duflo (Université Paris 7-Denis Diderot, Paris)

No lecture notes exist. A list of references can be found at the end

Lecture 1 SUPERALGEBRAS

• Commutative superalgebras and supermanifolds.

• Lie superalgebras. Lie superalgebras in differential geometry.

• Lie superalgebras in deformation theory.

Lecture 2 LIE SUPERGROUPS

• The supergroup GL(m,n), the Berezinian, exponential mapping.

• An application of the Berezinian: Berezin integral.

Lecture 3 CLASSICAL LIE SUPERALGEBRAS

• Examples of Lie superalgebras

• Structure of Lie superalgebras

Lecture 4 REPRESENTATIONS OF LIE SUPERALGEBRAS

References

F. A. Berezin, Introduction to Superanalysis.

Reidel Publishing Company, 1987.

I. N. Bernstein, Lecture on supersymmetry (1996)

http://www.math.ias.edu/drm/QFT/fall

L. Corwin, Y. Ne'eman and S. Sternberg, Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)

Reviews of modern physics ,47 (1975) 573-603

P. Deligne and J. W. Morgan, Notes on supersymmetry(following Josph Bernstein) In Quantum fields and strings: A course for mathematicians, AMS 1999

B. DeWitt, Supermanifolds,

Cambridge University Press, 1984

L. Frappat, A. Sciarrino and P. Sorba, Dictionary on Lie algebras and superalgebras.

Academic Press, 2000

V. G. Kac, Lie superalgebras,

Adv. Math. 26 (1977) 8-96

Yu. I. Manin, Gauge field theory and complex geometry,

Springer 1988

M. Scheunert, The theory of Lie superalgebras,

Lecture Notes in Mathematics 716 (1979)