Minimal free resolutions and Betti diagrams of the algebras of $SL_2$-invariants

TL;DR

This paper computes minimal free resolutions and Betti diagrams for algebras of $SL_2$-invariants with small homological dimension, providing detailed algebraic invariants.

Contribution

It offers explicit calculations of resolutions and Betti diagrams for specific $SL_2$-invariant algebras, advancing understanding of their algebraic structure.

Findings

Resolutions for small homological dimension cases

Betti diagrams detailing algebraic invariants

Enhanced understanding of $SL_2$-invariant algebra structures

Abstract

For the algebras of $SL_2$-invariants of small homological dimension theirs minimal free graded resolutions and graded Betti diagrams calculated.