Date:

Wed, 10/06/202011:00-13:00

Location:

Zoom - ID: 951 5522 0236 Password: 387201

Kobi Peterzil will speak about

**the infinitesimal subgroup of a simple real Lie group.**

(w. Martin Bays)

(w. Martin Bays)

__Abstrract:__

A theorem with Pillay and Starchenko (2000) says that If G is a simple linear Lie group then the pure group (G,.) is either:

(i) unstable, and then bi-interpretable with the real field, e.g when G is compact,

or

(ii) stable, and then bi-interpretable with the complex field.

Viewing G inside a big real closed field R, we let mu_G be the subgroup of infinitesimals of the identity, with respect to the archimedean valuation ring. Thus, the subgroup mu_G is definable in the associated Real Closed Valued Field (R,v) .

Theorem (w. Bays): For G compact and simple, the structure (mu_G,.) is bi-interpretable with (R,v).

I will discuss the setting and the proof of the above result. In addition, we propose the following generalization,

Conjecture: If G is a simple linear Lie group and (G,.) is unstable then mu_G is bi-interpretable with RCVF and if (G,.) is stable then mu_G is bi-interpretable with ACVF.