Dynamical Theory of Generalized Matrices

TL;DR

This paper introduces a generalized matrix framework based on multi-index objects, extending spin algebra and dynamical systems, with symmetries akin to volume-preserving diffeomorphisms in p-branes.

Contribution

It presents a novel generalization of spin algebra and matrix dynamics using multi-index objects, revealing new symmetry properties.

Findings

Solution described by generalized spin representation matrices

System exhibits symmetry similar to volume-preserving diffeomorphisms

Provides a new mathematical framework for extended matrix theories

Abstract

We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to the volume preserving diffeomorphism in the p-brane action.