Series: Mathematics Colloquium

Date: Thursday, March 4, 2004

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Host: Aissa Wade, Ping Xu

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Yvette Kosmann-Schwarzbach, Ecole Polytechnique, France

Title: Derived Brackets in Differential Geometry

Abstract:

  The Lie brackets of vector fields arise from the commutators of
  linear maps by a simple formula, going back to Henri Cartan (1950)
  if not further, which is valid more generally for the
  Schouten-Nijenhuis bracket of multivector fields.  We shall show
  that these formulas are examples of a "derived bracket
  construction", leading in general from Lie algebras to Leibniz
  algebras, and we shall illustrate this construction with examples
  from differential geometry.  If time permits, we shall sketch the
  more recent theory of "higher derived brackets".