The Berkovits Complex and Semi-free Extensions of Koszul Algebras

TL;DR

This paper explores the Berkovits complex and semi-free extensions of Koszul algebras, connecting string quantization ideas with algebraic homology calculations to advance understanding in algebraic topology and mathematical physics.

Contribution

It introduces a new complex that links Berkovits' string quantization approach with algebraic homology, bridging different mathematical perspectives.

Findings

Developed a complex for calculating homologies of Koszul algebras.

Connected Berkovits' ideas with algebraic and homological frameworks.

Provided tools for future research in algebraic topology and mathematical physics.

Abstract

In his extension of W. Siegel's ideas on string quantization, N. Berkovits made several observations which deserve further study and development. Indeed, interesting accounts of this work have already appeared in the mathematical literature and in a different guise due to Avramov. In this paper we bridge between these three approaches, by providing a complex that is useful in the calculation of some homologies.