# Algebras of Quasi-Pl\"ucker Coordinates are Koszul

## TL;DR

This paper introduces non-commutative algebras of quasi-Plücker coordinates, demonstrating they are Koszul by analyzing their quadratic duals with Gr"obner bases, thus providing new examples in algebra theory.

## Contribution

It establishes that these quasi-Plücker coordinate algebras are Koszul, expanding the class of known non-homogeneous quadratic Koszul algebras.

## Key findings

- Algebras of quasi-Plücker coordinates are Koszul.
- Quadratic duals have quadratic Gr"obner bases.
- Provides new examples of non-homogeneous quadratic Koszul algebras.

## Abstract

Motivated by the theory of quasi-determinants, we study non-commutative algebras of quasi-Pl\"ucker coordinates. We prove that these algebras provide new examples of non-homogeneous quadratic Koszul algebras by showing that their quadratic duals have quadratic Gr\"obner bases.