Representations of Color Lie Superalgebras by Hilbert Series

TL;DR

This paper studies the Hilbert series representations of color Lie superalgebras, providing formulas and methods to understand their structure and counting states in various degrees across different mathematical contexts.

Contribution

It introduces a dimension formula similar to Witt's formula for free color Lie superalgebras and explores specific classes of color Lie p-superalgebras.

Findings

Derived a dimension formula for color Lie superalgebras

Presented methods to compute Hilbert series for these superalgebras

Analyzed specific classes of color Lie p-superalgebras

Abstract

The representations of various color Lie superalgebras by Hilbert series are the main topic of this work. The Color Lie superalgebras appear in various branches of mathematics (e.g., topology, algebraic groups, etc.). They are generalized Lie superalgebras. A generating function known as the Hilbert series of color Lie superalgebras which encodes crucial knowledge about the superalgebras representation. In particular, it provides a way to count the number of states in the a given degree. We present a dimension formula that resembles Witt's formula for free color Lie superalgebras, and a specific class of color Lie p-superalgebras.