On the 13th of June 2019, at 10:15 a.m.
Daniel
Wysocki (KMMF)
will give a talk on
"Gradations,
Grassmann algebras, and modified classical
Yang-Baxter equations"
Abstract
A
coboundary Lie bialgebra is a Lie
algebra, g, equipped with a map δ
: v ∈ g → [v, r] ∈Λ^2g, where [·,
·] is the algebraic Schouten
bracket on the Grassmann algebra
Λg and r ∈ Λ^2g is a solution of
the modified classical Yang–Baxter
equation (MCYBE), i.e. [v, [r, r]]
= 0 for every v ∈ g. The
classification and properties of
solutions of the MCYBE are
well-studied mostly for semisimple
Lie algebras or when dim g ≤ 3. To
tackle non-semisimple and
higher-dimensional cases, one
needs new tools. In this talk, I
will discus the use of gradations
on g and Λg in finding solutions
and studying the structure of the
MCYBE. Several examples will be
presented to illustrate this
approach.
The seminar takes place on Thursdays from 10:15 a.m. to
12:00 in the room 2.23 of the main building of the
Faculty of Physics (the 2nd floor), Pasteur Str. 5,
Warszawa.
Additional information can be found on the webpage http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.
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