Jan-Erik Roos: Classical Lie algebras contra infinite-dimensional positively graded Lie algebras

Jan-Erik Roos, Stockholm university

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Time: Wed 2013-02-06 kl 14.15 - 16.15

Location: Room FB53 and Oskar Klein auditorium, Albanova


14:15-15:00: Precolloquium for PhD and master students by Alexander Berglund. (Room FB53, Roslagstullsbacken 21.)

15:15-16:15: Colloquium lecture by Jan-Erik Roos. (Oskar Klein auditorium.)

16:15-17:00: Coffee and SMC social get-together.

Abstract (Colloquium)

Finite-dimensional Lie algebras have a long history going back to Lie, Killing, Elie Cartan, ... I will start with a short survey of their theory. Then I will pass to the main subject of my talk, namely those infinite-dimensional positively graded graded Lie algebras that come up in

    Group theory,
    Algebraic topology,
    Commutative ring theory.

For a long time it seemed impossible to say something in these three cases if you were inspired by the finite-dimensional case. But this has now changed and I will give explicit examples illustrationg this. The phenomena that I will describe have in some cases been found and inspired by computer calculations using a programme liedim which has been written by Clas Löfwall. My main emphasis will be case 1) above, but the precolloquium talk 14.15-15.00 by Alexander Berglund will put more emphasis on the other cases.