G-twisted braces and orbifold Landau-Ginzburg Models

TL;DR

This paper develops brace structures for G-twisted Hochschild cochains of algebras with group actions and applies these to construct G-Frobenius algebras for orbifold Landau-Ginzburg B-models, providing explicit formulas.

Contribution

It introduces new brace structures for G-twisted Hochschild cochains and applies them to orbifold Landau-Ginzburg models, offering explicit product formulas.

Findings

Constructed brace structures for G-twisted Hochschild cochains.

Built G-Frobenius algebras for orbifold Landau-Ginzburg B-models.

Derived explicit orbifold cup product formulas for invertible polynomials.

Abstract

Given an algebra with group $G$-action, we construct brace structures for its $G$-twisted Hochschild cochains. An an application, we construct $G$-Frobenius algebras for orbifold Landau-Ginzburg B-models and present explicit orbifold cup product formula for all invertible polynomials.