# Excellence in Research: Quantum nilpotent algebras and essential sets

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · North Carolina Central University (NC) · $417,333

## Abstract

Quantum algebras are mathematical objects that arose from problems in quantum physics. In many instances, they are constructed by deforming the structure of classical algebras, which serve as mathematical models in classical physics. The quantum structure is usually noncommutative (meaning the variables do not commute with each other), whereas the classical structure is commutative (the variables commute). Quantum algebras have since played important roles in several areas of mathematics, including topology, statistical mechanics, and noncommutative algebraic geometry.  This research project studies key questions involving the algebraic structures and symmetries of various classes of these algebras. The work also pursues related questions about Fulton's essential sets. These are combinatorial objects that originated in the early 1990's from problems in Schubert calculus, and have since appeared in various mathematical contexts, including Lie theory and Coxeter group theory. The research aims to advance, and to strengthen connections among, these interrelated areas.  This project expands opportunities for student research involvement at North Carolina Central University.

Specifically, this Principal Investigator will study relationships between quantum nilpotent algebras and Fulton's essential sets, and explore applications to representation theory and other structural properties, particularly automorphisms, of these algebras. The major research goals of this project inc

## Key facts

- **NSF award ID:** 2502817
- **Awardee organization:** North Carolina Central University (NC)
- **SAM.gov UEI:** L1DXXP1KGP77
- **PI:** Garrett Johnson
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $417,333
- **Funds obligated:** $417,333
- **Transaction type:** Standard Grant
- **Period:** 08/15/2025 → 07/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2502817

## Citation

> US National Science Foundation, Award 2502817, Excellence in Research: Quantum nilpotent algebras and essential sets. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2502817. Licensed CC0.

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