Pasha Zusmanovich
Tallin University,Estonia
Lie algebras coming from dual operads and their invariants.
Abstract: I will discuss Lie algebras arising as tensor products of two algebras over binary quadratic operads Koszul dual to each other. Many Lie algebras appearing in physics - including "Poisson brackets of hydrodynamic type" of Balinsky-Novikov, Schrödinger-Virasoro algebra, etc. - admit representation in such a form for a suitable pair of dual operads. I will also speculate on a possible role of this tensor product construction in the structure theory of Lie algebras in small characteristics. A simple linear-algebraic method, somewhat resembling separation of variables of differential equations, allows, in some situations, to compute invariants of such Lie algebras which are important for physics and structure theory - such as low-degree cohomology, invariant bilinear forms, etc.