Order structures on enveloping algebras

SCOSAAR course for PhD students

February - May 2012

Instructor: Daniel Beltita

Class schedule and location:

Wednessday 12:00-14:00, Room 414 (IMAR)

Topics:

1. Lie groups and Lie algebras

2. Invariant differential operators on Lie groups

3. Enveloping algebras: basic definitions; the Poincaré-Birkhoff-Witt theorem

4. Algebras of distributions with compact support on Lie groups

5. Differentiability of vectors with respect to Lie group representations

6. Functions and distributions of positive type

7. Moment problems on Lie groups

Supplementary reading:

K. Schmüdgen, Positive cones in enveloping algebras. Reports on Mathematical Physics 14 (1978). no. 3, 385--404.

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