La th\'eorie des invariants des formes quadratiques ternaires revisit\'ee

TL;DR

This paper revisits the invariants of multiple ternary quadratic forms under the special linear group, providing explicit descriptions using Jordan algebra structures, building on historical symbolic methods.

Contribution

It offers explicit formulas for invariants of several ternary quadratic forms using Jordan algebra, enhancing previous symbolic approaches.

Findings

Explicit invariants for 2-5 ternary quadratic forms derived

Utilizes Jordan algebra structure for clarity and explicitness

Builds on and refines classical symbolic invariant methods

Abstract

The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan algebra structure of the space of ternary quadratic forms, we give these invariants explicitely.