Quadratic linear algebras associated with factorizations of noncommutative polynomials and noncommutative differential polynomials

Selecta Mathematica, New Series

Volumn 7, Issue 4, 2001, Pages 493-523

  Gelfand, Israel ^a   Retakh, Vladimir ^a   Wilson, Robert Lee ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Differential polynomials; Noncommutative polynomials; Quadratic linear algebras

Indexed keywords

EID: 52549093774     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s00029-001-8096-5     Document Type: Article

References (16)

1. [BW] U. Bray and G. Whaples. Polynomials with Coefficients from a Division Ring. Canadian J. Math. 35 (1983), 509-515.
2. [C1] P.M. Cohn. Skew Field Constructions. Cambridge Univ. Press, 1977.
3. [C2] P.M. Cohn. Skew Fields. Cambridge Univ. Press, 1995.
4. [CS] A. Connes and A. Schwarz. Matrix Vieta Theorem revisited. Letters in Math. Physics 39 (1997), 349-353.
5. [EGR] P. Etingof, I. Gelfand and V. Retakh. Factorization of Differential Operators, Quasideterminants, and Nonabelian Toda Field Equations. Math. Research Letters 4 (1997).
6. [FS] D. Fuchs and A. Schwarz. Matrix Vieta Theorem, in: Lie groups and Lie algebras: E.B. Dynkin Seminar (1995), 15-22.
7. [GKLLRT] I. Gelfand, D. Krob, A. Lascoux, V. Retakh and J.-Y. Thibon. Noncommutative Symmetric Functions. Advances in Math. 112 (1995), 218-348.
8. [GR1] I. Gelfand and V. Retakh. Determinants of matrices over noncommutative rings. Fund. An. Appl. 25 (1991), 91-102.
9. [GR2] I. Gelfand and V. Retakh. A theory of noncommutative determinants and characteristic functions of graphs. Fund. An. Appl. 26 (1992), 1-20.
10. [GR3] I. Gelfand and V. Retakh. Noncommutative Vieta theorem and symmetric functions. In: Gelfand Math. Seminars 1993-95. Birkhauser, Boston, 1996.
11. [GR4] I. Gelfand and V. Retakh. A theory of noncommutative determinants and characteristic functions of graphs. I. In: Publ. LACIM, UQAM, vol. 14, 1993, 1-26.
12. [GR5] I. Gelfand and V. Retakh. Quasideterminants, I. Selecta Math. 3 (1997), 417-546.
13. [J] N. Jacobson. Lie Algebras. Wiley Interscience, New York-London, 1962.
14. [L] T.Y. Lam. A First Course in Nonncommutative Rings. Springer-Verlag, New York, 1991.
15. [O] O. Ore. Theory of Non-commutative Polynomials. Annals Math. 34 (1933), 480-508.
16. [W] R.L. Wilson. Invariant Polynomials in the Free Skew Field. Selecta Math 7, 565-586.