EA-Matrix Integrals of Associative Algebras and Equivariant Localization

Serguei Barannikov (1, 2, 3, 4, 5)

1 IMJ - Institut de Mathématiques de Jussieu
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 CNRS - Centre National de la Recherche Scientifique
4 UPCité - Université Paris Cité
5 SU - Sorbonne Université

I consider the simplest examples of the equivariantly closed matrix integrals introduced in [B06], corresponding to super associative algebras with an odd trace. I prove that the EA-matrix integrals for associative algebras with scalar product are integrals of equivariantly closed differential forms with respect to the Lie algebra $gl_N(A)$.

Mots clés: Mirror symmetry; Gromov-Witten invariants; Noncommutative varieties; Batalin-Vilkovisky formalism

Domaines: Géométrie algébrique [math.AG]; Géométrie symplectique [math.SG]; Physique mathématique [math-ph]

Serguei Barannikov. EA-Matrix Integrals of Associative Algebras and Equivariant Localization. Arnold Mathematical Journal, 2010, 2019 (5), pp.97-104. ⟨10.1007/s40598-019-00111-0⟩. ⟨hal-00507788v2⟩