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Extra Colloquium Mathematics, Prof. dr. D.A. Leites (Stockholm)

12 June 2014

Join us for coffee and tea at 13.45 p.m.

Date:                      

Thursday, June 12th 2014

Speaker:

Prof. dr. D.A. Leites (Stockholm)

Room:

5161.0253 (Bernoulliborg)

Time:

14.00

Title: Towards classification of simple Lie algebras and Lie superalgebras.


Abstract:

  Over complex numbers, the simple Lie algebras are classified in the following cases: finite-dimensional, infinite-dimensional and Z-graded in the two cases: if they are of polynomial growth and if they are ``almost affine", a.k.a. hyperbolic.   The simple Lie superalgebras in the above cases are classified except for infinite-dimensional and Z-graded of polynomial growth, where the answer (of which I am sure) is conjectural.   Over algebraically closed fields of characteristic p>3, the simple finite-dimensional Lie algebras are classified. They are usually obtained by a procedure due to Kostrikin and Shafarevich, which I will reformulate to embrace (conjecturally) p=3.   For p=2, to obtain simple Lie algebras we need to incorporate Lie superalgebras. And the other way round. Huge amount of computations needed to find out deformations hamper the advancement of classification. I'll retell one (or two, time permitting) procedures that from every simple Lie algebra makes a simple Lie superalgebra, most of them new until this (22nd) week of 2014.   Observe that Lie superalgebras appeared in mathematics not in 1970 over fields of real or complex numbers, borrowed from works of physicists, but in topology, in 1930s, over finite fields.

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
Dr. A.V. Kiselev (e-mail: a.v.kiselev@rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/

Last modified:06 June 2018 2.04 p.m.

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