Publications of Vladimir Retakh

  1. The dual space to a subspace of countable inductive limit. Doklady AN SSSR(=Soviet Mathematics Doklady), 184 (1969), 44-46

  2. The adjoint homomorphism of locally convex spaces. Funct. analiz i ego prilozh. (=Funct. analysis. Applications), 3, (1969), n 4, 63-68

  3. The subspaces of a countable inductive limit. Doklady AN SSSR, 194, (1970), 1277-1279

  4. The problem of moments in locally convex spaces. Doklady AN SSSR, 209, (1972), 562-564

  5. Homological methods in a theory of locally convex spaces. Thesis, 1973, 130 pp.

  6. Versal deformations of germs of holomorphic mappings. Funct. analiz i ego prilozh., 8, (1974), n 1, 86-87

  7. An abstract analog of the theorem on the existence of solutions of convolution equations (with V. Ptak). Doklady AN SSSR (=Soviet mathematics Doklady), 216, (1974), 267-269

  8. A remark on functor Ext in locally convex spaces. Uspehi matem. nauk (=Russian math. Surveys), 31, (1976), n 4 , 271-272

  9. On a theorem of Eidelheit. Siberian math. J., 17, (1976), n 6, 1367-1381

  10. The Massey operations in Lie superalgebras, and deformatios of complex-analytic algebras. Funct. analiz i ego priloz. (=Funct. analysis. Applications), 11, (1977), n 4, 88-89

  11. Singular supports. I (with V. Ptak). Casopis pro pestovan. math., 104, (1977), n 1, 382-388

  12. The structure of Lie superalgebras with the semisimple even part (with. F.A. Berezin). Funct.analiz i ego priloz. (=Funct. analysis. Applications, 12, (1978), n 1, 64-65

  13. Massey operations in Lie superalgebras and differentials of the Quillen spectral sequence. Funct.analiz i ego priloz. (=Funct. analysis. Applications,, 12, (1978), n 4, 91-92

  14. Construction of Lie superalgebras with a semisimple even part (with F.A. Berezin). Vestnik of Moscow State University, (1978), n 5, 63-67

  15. Massey operations, obstructions to formality in Sullivan's sense and obstructions to Kodaira-Spencer deformations. Uspehi matem. nauk (=Russian Math. Surveys), 35, (1980), n 3, 217-220

  16. A method of computings of characteric classes of bundles (with F.A. Berezin). Reports on mathematical physics., 17, (1980), n 3, 363-378

  17. Cohomology of some Lie algebras and Lie superalgebras of vector fields (with B.L. Feigin). Uspehi matem. nauk (=Russian Math. Surveys), 37, (1982), n 2, 233-234

  18. Operations de Massey, la construction S et extensions de Yoneda. C.R. Acad. Sc. Paris, 299, (1984), Ser. 1, n 11, 475-478

  19. Massey operations in Lie superalgebras and differentials in the Quillen spectral sequence. Colloquium mathematicum, 50, (1985), n 1, 81-94

  20. Topology of Linked Defects in Condensed Matter (with M.I. Monastyrsky). Commun. Math. Physics, 103, (1986), n 3, 445-459

  21. New topology invariants of linked linear defects in condensed matter (with M.I. Monastyrsky), in: Group theoretical methods in physics. Proceedings of the third seminar. Yurmala, May 22-24, 1985. Moscow, Nauka, 1986, 661-670

  22. Homotopical properties of category of extensions. Uspehi matem. nauk (=Russian Math. Surveys), 41, (1986), n 6, 179-180

  23. Generalized Airey functions, Shubert cells and Jordan groups (with I.M.Gelfand and V.Serganova). Doklady AN SSSR (=Soviet mathematics Doklady), 298, (1988), n 1, 8-12

  24. The fundamental affine space and canonical basis in irreducible representations of the group Sp4 . (with A.V.Zelevinsky). Doklady AN SSSR (=Soviet mathematics Doklady), 300,(1988), n 1, 31-35

  25. Massey operations in the cohomology of infinite-dimensional Lie algebra  L1 (with B.L.Feigin and D.B.Fuchs). in: Lecture Notes in Math.,1346, (1988), 13-31

  26. Reduction formulas for hypergeometric functions on the Grassmanian Gk,n  and the description of hypergeometric functions on strata of small codimension in Gk,n. (with I.M.Gelfand, M.I Graev). Doklady AN SSSR, 318, (1991), n 4, 793-797.

  27. Gamma -series and general hypergeometric functions on the manifold of  k × n - matrices (with I.M.Gelfand, M.I Graev). IPM Preprint N 64. 27pp , Moscow, 1990.

  28. Hypergeometric functions on small codimensional strata in Grassmanian Gk,n. (with I.M.Gelfand, M.I Graev). IPM Preprint N 138. 25 pp, Moscow, 1990

  29. Hypergeometric functions on the k th exterior power of the space Cn  and the Grassmanian Gk,n   and the connection between them. (with I.M.Gelfand, M.I Graev). Doklady AN SSSR, 320, (1991), n 1, 20-24

  30. Recent developments in the theory of hypergeometrical functions. (with I.M.Gelfand, M.I Graev). Report of Taniguchi symposium, Kyoto, Japan, 1991.

  31. Determinants of matrices over noncommutative rings. (with I.M.Gelfand). Functional Anal. Appl. 25, (1991), n 2, 13-25

  32. Generalized hypergeometric functions connected with an arbitrary finite or locally compact continuous field. (with I.M. Gelfand, M.I Graev). Doklady RAN,323, (1992), n 3, 394-397

  33. Theory of noncommutative determinants and characteristic functions of graphs . (with I.M. Gelfand). Functional Anal. Appl. 26, (1992), n 4, 1-20

  34. Difference analogues and q-analogues of general hypergeometric systems of differential equations. (with I.M. Gelfand, M.I Graev). Doklady RAN, 325, (1992), n 2, 215-220

  35. General hypergeometric systems of equations and series of hypergeometric type. (with I.M. Gelfand, M.I Graev). Russian Math. Surveys, 47, (1992), n 4, 3-82

  36. Theory of noncommutative determinants and characteristic functions of graphs.(with I.M. Gelfand). I. Publ. LACIM, UQAM, Montreal, 14,(1993), 1-26

  37. Reduction formulas for hypergeometric functions associated with with the Grassmanian  Gk,n and description of these functions on strata of small codimension in Gk,n. Russian J. on Math. Phys., 1 , n 1, 19-56 (1993)

  38. Lie-Massey brackets and n-homotopically multiplicative maps of differential graded Lie algebras, Journal of Pure and Applied Algebra, 89 , (1993), n 1-2, 217-229

  39. Hypergeometric functions on the k-th external power  of  Cn and on the Grassmanian Gk,n, their relationships and integral representations. (with I.M.Gelfand, M.I Graev). Russian J. on Math. Phys., 1 , (1993), n 3, 289-311

  40. The Schwarz derivative for noncommutative differential algebras. (with N.Shander), in: Advances in Soviet Math., 17, (1993), 139-154

  41. The q-hypergeometric Gauss equation and the description of its solutions in the form of series  and integrals. (with I.M. Gelfand, M.I. Graev). Doklady RAN, 331, (1993) , n 2, 140-143

  42. Hypergeometric systems of equations of Gelfand-type equations and series in orthogonal polynomials.(with M.I. Graev). Letters in Math. Phys., 28, (1993) , 195-205

  43. (r,s) -hypergeometric functions of one variable. (with I.M. Gelfand, M.I. Graev). Doklady RAN, 333,(1993) , n 5, 567-570

  44. On $(r,s)$-differential calculus, $(r,s)$-hypergeometric functions and quantum group $GL_{r,s}(2) $. Preprint 1993 (with I.M. Gelfand, M.I. Graev and S.A. Spirin)

  45. (r,s) -exponents. (with I.M. Gelfand, M.I. Graev and S.A. Spirin). Doklady RAN, 336, (1994), n 6, 730-732

  46. Noncommutative symmetric functions. (with I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc and J.-Y.Thibon). Advances in Math, 112, (1995), n 2, 218-348

  47. A noncommutative Vieta theorem and symmetric functions, (with I.M. Gelfand), in: The Gelfand Mathematical Seminars 1993-1995, Birkhauser, Boston, 1995 , 93-100

  48. Extension Categories and their Homotopy. (with Amnon Neeman). Compositio Mathematica, 102,(1996), 203-242

  49. Some applications of quasideterminants to combinatorics, in preparation (with I. Pak and A. Postnikov)

  50. Quasideterminants, I. (with I.M. Gelfand). Selecta Math., 3, (1997), n 4, 517-546,

  51. Factorisation of differential operators, quasideterminants, and nonabelian Toda field equations. (with P. Etingof and I.M. Gelfand). Math. Research Letters, 4, (1997), n 2-3, 413-425

  52. Editor (with V.Arnold, I. Gelfand, M. Smirnov). The Arnold-Gelfand Mathematical Seminars. Geometry and Singularity Theory. Birkhauser, 1997

  53. General gamma-functions, exponentials and hypergeometric functions. (with I.M. Gelfand and M.I. Graev). Russian Math. Surveys, 53,(1998), n 1, 3-60

  54. Chi-Han Sah (1934-1997). (with. J. Dupont, A. Phillips, J. Roitman, and M. Saul). Notices AMS, 45,(1998), n 1,79-83

  55. Nonabelian integrable systems, quasideterminants, and Marchenko lemma. (with P. Etingof and I. Gelfand). Math. Research Letters, 5, (1998), n 1-2, 1-12

  56. Fedosov manifolds. (with I. Gelfand and M. Shubin). Advances of Mathematics, vol.136,(1998), 104-140

  57. Quantum determinants and quasideterminants. (with P.Etingof). Asian J. of Math., 3,(1999), n 2, 345-352

  58. Noncommutative rational functions and Farber's invariants of boundary links. (with. C. Reutenauer and A. Vaintrob), in: Differential topology, infinite-dimensional Lie algebras, and applications, Amer Math Soc Transl., 194, (1999), 237-246

  59. Editor (with I. Gelfand). The Gelfand Mathematical Seminars 1996-1999, Birkhauser, 2000

  60. Quadratic-linear algebras associated with decompositions of noncommutative polynomials and noncommutative differential polynomials. (with I. Gelfand and R. Wilson). math.QA/0002238, Selecta Math., 7, (2001), 493-523

  61. Noncommutative algebras associated to complexes and graphs. (with I. Gelfand and S. Gelfand), math.QA/0008090, Selecta Math., 7, (2001), 525-531

  62. Hilbert series of quadratic algebras associated with decompositions of noncommutative polynomials (with I. Gelfand, S. Gelfand, S. Serconek, and R. Wilson), math.QA/0109007, J. of Algebra, 254, (2002), n 2, 279-299

  63. Quaternionic quasideterminants and determinants (with I. Gelfand, R. Wilson), math.QA/0206211, in: Lie Groups and Symmetric Spaces, Amer. Math. Soc. Transl.-Ser. 2, (2003), n 210

  64. Quasideterminants and Casimir elements for the general Lie supealgebras (with A. Molev), Intern. Math. Res. Notes, (2004), n 13, 611-619.

  65. Hypergeometric functions over an arbitrary field (with I. Gelfand, M. Graev), Russian Math. Surv., vol 59 (2004), no 5, 29-100

  66. Quasideterminants (with I. Gelfand, S. Gelfand and R. Wilson), Advances in Math. (2005), vol. 193, no 1, 56-141

  67. Gauss q-hypergeometric equation and its solution as series and integrals (with I. Gelfand, M. Graev), Russian J. Math. Physics, vol 12 (2005), vol. 12, no 2, 168-179

  68. Noncommutative double Bruhat cells and their factorizations (with A. Berenstein), Imtern. Math. Res. Notes, (2005), n 8, 477-516

  69. On a class of algebras associated to directed graphs (with I. Gelfand, S. Serconek, R. L. Wilson), Selecta Math., (2005), vol 11, no 2, 281-295

  70. Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs (with I. Gelfand, S. Gelfand, R. L. Wilson), Lett. Math. Physics, (2005), vol. 74, Issue 2, 153-167

  71. Editor (with P. Etingof, I. Singer), The Unity of Mathematics, In Honor of Ninetieth Birthday of I.M. Gelfand, Progress in Math., vol. 244, Birkhauser, 2005

  72. On a class of Koszul algebras associated to directed graphs (with S. Serconek, R. L. Wilson), J. of Algebra, (2006), vol. 304, 1114-1129

  73. Noncommutative loops over Lie algebras (with A. Berenstein), preprint MPIM, (2006), no 131

  74. Hilbert series of algebras associated to directed graphs (with S. Serconek, R. L. Wilson), J. of Algebra, (2007), vol. 312, 142-151

  75. Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials (with S. Serconek, R. L. Wilson), Proceedings of the Conference "Lie Algebras, Vertex Operator Algebras and Their Applications",Contemp. Math., 2007, vol. 442, 201-219

  76. Advanced course on quasideterminants and universal localization, Notes of the course (with R. L. Wilson), 124 pp, CRM, Barcelona, 2007

  77. Lie algebras and Lie groups over noncommutative rings (with A. Berenstein), Advances in Math., 2008, vol. 218, no 6, 1723-1758

  78. Algebras associated to directed acyclic graphs (with R.L. Wilson), Advances in Applied Mathematics, 2009, vol. 42, no 1, 42-59

  79. Codes and Noncommutative Stochastic Matrices (with S. Lavallée, C. Reutenauer, and D. Perrin), J. of Noncommutative Geometry, no 4, 2010, 531-554

  80. Koszulity of splitting algebras associated with cell complexes (with S. Serconek, R. Wilson), Journal of Algebra, vol. 323 (2010), pp. 983-9

  81. From factorizations of noncommutative polynomials to combinatorial topology, Central European J. Math., vol. 8 (2010), 235-243

  82. Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation (with V. Rubtsov), J. of Physics A, vol 43(2010), no 505204

  83. A Spectral Theory for Tensors (with E. K. Gnang, A. Elgammal), Annales de la Faculté des Sciences de Toulouse Mathematique, Sér. 6, vol. 20, no. 4 (2011), p. 801-841

  84. A short proof of Kontsevich cluster conjecture (with A. Berenstein), Comptes Rendus Acad. Sci., Ser. I, vol 349 (2011), p. 119-122

  85. Hilbert series of algebras associated to direct graphs and order homology (with S. Serconek, R. Wilson), J. of Pure Applied Algebra, vol. 216, no 6 (2012), p. 1397-1140

  86. The Reciprocal of $\sum_{n\geq 0}a^nb^n$ for non-commuting $a$ and $b$, Catalan numbers and non-commutative quadratic equations (with A. Berenstein, C. Reutenauer, and D. Zeilberger), Contemporary Mathematics, vol 592 (2013)

  87. Editor (with A. Berenstein) ``Noncommutative Birational Geometry, Representations and Combinatorics", American Math. Soc, 2013, 250 pp.

  88. Noncommutative Laurent phenomenon, triangulations and surfaces, Oberwolfach Report 58/2013, p. 39--41

  89. Noncommutative cross-ratios, Journal of Geometry and Physics, vol. 82, August 2014, p. 13--17.

  90. Generalized adjoint actions (with A. Berenstein), J. Lie Theory, vol 26 (2016), p. 219--225

  91. Algebras of quasi-Pl\"ucker coordinates are Koszul (with R. Laugwitz), J. Pure Applied Algebra, vol 222 (2018), p. 2810--2822

  92. Noncommutative marked surfaces (with A. Berenstein), Advances in Math., vol 328 (2018), p. 1010--1087

  93. Noncommutative Catalan numbers (with A. Berenstein), Annals of Combinatorics, vol. 23 (2019), pp.527-547

  94. Noncommutative shifted symmetric functions (with R. Laugwitz), Moscow Math. J., vol. 20 (2020), pp.1-24

  95. Noncommutative cross-ratio and Shwarz derivative (with V.Rubtsov and G.Sharygin), Integrable Systems and Algebraic Geometry, Lecture Notes London Math. Soc., Vol. 459 (2020), pp.499-528

  96. On the rational relationships among pseudo-roots of a noncommutative polynomial (with M. Saks), J. Pure Appl. Algebra, vol. 225 (2021), no. 6, Paper No. 106581, 15 pp.

  97. Symplectic groups over noncommutative algebras (with D. Alessandrini, A. Berenstein, E. Rogozinnikov, A. Wienhard), Selecta Math. vol. 28(2022), no. 4, Paper No. 82, 119 pp

  98. A fully noncommutative analog of the Painleve IV equation and a structure of its solutions (with I. Bobrova, V. Rubtsov, G. Sharygin), Journal of Physics A vol. 55 (2022) no. 47, Paper No. 475205, 30 pp

  99. Non-Abelian discrete Toda chains and related lattices, (with I.Bobrova, V.Rubtsov, G.Sharygin), arxiv:2311.11124, 36 pp

  100. Noncommutative clusters (with A. Berenstein), in preparation, posted at http://pages.uoregon/edu/arkadiy/noncomtriangpub.pdf

      Return to Vladimir Retakh's home page