Quasideterminants

2002/08/21 by I. Gelfand, Gelfand, I., S. Gelfand +5 · 7 citations
Mathematics · #05E05 #15A15 #16W30 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:05E05 #msc:15A15 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0208146

amstex; final version; to appear in Advances in Math

arxiv created 2004/08/06 · arxiv updated 2009/11/30

Abstract

The determinant is a main organizing tool in commutative linear algebra. In this review we present a theory of the quasideterminants defined for matrices over a division algebra. We believe that the notion of quasideterminants should be one of main organizing tools in noncommutative algebra giving them the same role determinants play in commutative algebra.

Cited by

• Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
• Tau functions of the constrained matrix KP hierarchy
• Non-commutative multiple bi-orthogonal polynomials: formal approach and integrability
• Darboux transformations and related non-Abelian integrable differential-difference systems of the derivative nonlinear Schrödinger type
• Asymptotics for the noncommutative Painlevé II equation
• Dualities of Gaudin models with irregular singularities for general linear Lie (super)algebras
• Bethe algebras for unitarizable modules over classical Lie (super)algebras and a duality

Related

• Quaternionic quasideterminants and determinants
• Matrices over polynomial rings approached by commutative algebra
• Biring of Matrices
• Unifying Linear Algebra
• Noncommutative Spectral Decomposition with Quasideterminant