Graded Necklace Lie Bialgebras & Batalin-Vilkovisky Formalism (Nikolai PERRY, Edinburgh)

25.06.2024 15:30 – 16:30

The necklace Lie bialgebra is constructed from the double of a quiver. Its Lie bracket has been related to a canonical Poisson structure on the representation variety of the double quiver via a trace map. What about the Lie cobracket?

By encoding the necklace Lie bialgebra in a Batalin-Vilkovisky (BV) algebra 'B', we show that the Lie cobracket can be viewed from the perspective of a suitable representation variety. This representation variety carries a non-degenerate pairing, inducing a canonical BV operator on a quotient of its algebra of functions 'O' — we construct a BV algebra morphism B --> O which preserves information of both the necklace bracket and cobracket.

In addition, we generalise the necklace Lie bialgebra, as well as the above construction, to the Z_2-graded setting.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre