Quadratic-linar algebras associated with factorizations of noncommutative polynomials and noncommutative differential polynomials

2000/02/28 by Israel M. Gelfand, Israel Gelfand, Gelfand, Israel +4
Mathematics · #05E05 #15A15 #16W30 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:05E05 #msc:15A15 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0002238

30 pages, last revision

openalex publication_date 2000/02/28 · arxiv created 2001/10/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and differential polynomials. Such algebras posses a natural derivation and give us a new understanding of a nature of noncommutative symmetric functions.

Citations

• Theory of Non-Commutative Polynomials

Related

• Noncommutative symmetric functions
• Noncommutative algebras associated to complexes and graphs
• Algebras associated to pseudo-roots of noncommutative polynomials are Koszul
• Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials
• Noncommutative Plurisubharmonic Polynomials Part I: Global Assumptions