EA-Matrix integrals of associative algebras and equivariant localization

TL;DR

This paper investigates EA-matrix integrals within graded associative algebras, demonstrating they are integrals of equivariantly closed forms under certain Lie algebra actions, extending previous work on equivariantly closed matrix integrals.

Contribution

It proves that EA-matrix integrals for associative algebras with scalar products are integrals of equivariantly closed differential forms under the action of the Lie algebra $gl_N(A)$.

Findings

EA-matrix integrals are equivariantly closed differential form integrals.

Extension of equivariantly closed matrix integrals to graded associative algebras.

Provides a mathematical framework connecting associative algebra structures with equivariant localization.

Abstract

Preprint HAL-00507788 (2010) from the CNRS open online arxive HAL. The equivariantly closed matrix integrals introduced in [B06], are studied in the case of the graded associative algebras with odd or even scalar product.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 $gl_N(A)$.