Publications by Volodymyr Lyubashenko

Monographs

• I. Squared Hopf algebras, Mem. Amer. Math. Soc. 142 (1999) n. 677, 184 p.
  
• II. Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners, Lect. Notes in Math., vol. 1765, Springer-Verlag, Heidelberg, 2001, vi+379 p. (with T. Kerler).
  
• III. Pretriangulated A_infinity-categories, Proceedings of the Institute of Mathematics of NAS of Ukraine, vol. 76, Institute of Mathematics of NAS of Ukraine, Kyiv, 2008, 599 p. The version presented here has different number of pages, but the numbering of sections and formulae is final (with Yu. Bespalov and O. Manzyuk).
  Corrections to the published version of the book (already fixed in the electronic version).
  
• IV. Curved cooperads and homotopy unital A_infinity-algebras, Math. Studies Monograph Series, vol. 17, VNTL Publishers, L'viv, 2015, viii+196 p.
  

  Articles, available on the net

• 7. Fourier transform identities in quantum mechanics and the quantum line, Phys. Lett. B284 (1992) 66-70 (with S. Majid).
  
• 8. Braided Groups and Quantum Fourier Transform, J. Algebra 166 (1994) n. 3, 506-528 (with S. Majid).
  
• 9. Existence of R-matrix for quantized Kac-Moody algebra, Math. Proc. Cambridge Philos. Soc. 116 (1994) n. 2, 193-207.
  
• 10. Quantum Function Algebra at Roots of 1, Adv. in Math. 108 (1994) n. 2, 205-262 (with C. De Concini).
  
• 13. Modular properties of ribbon abelian categories, Symposia Gaussiana, Proc. of the 2nd Gauss Symposium, Munich, 1993, Conf. A, Eds.: Behara, Fritsch, Lintz, Walter de Gruyter: Berlin, New York 1995, 529-579. [abs, src, ps]
  
• 14. Invariants of 3-Manifolds and Projective Representations of Mapping Class Groups via Quantum Groups at Roots of Unity, Commun. Math. Phys. 172 (1995) 467-516. [abs, src, ps]
  
• 15. Ribbon Abelian Categories as Modular Categories, J. Knot Theory Ramif. 5 (1996) n. 3, 311-403.
  
• 16. Extensions and Contractions of the Lie Algebra of q-Pseudodifferential Symbols on the Circle, J. Funct. Anal. 143 (1997) n. 1, 55-97 (with B. Khesin and C. Roger). [abs, src, ps]
  
• 17. Squared Hopf algebras and reconstruction theorems, Proc. of the Workshop ``Quantum Groups and Quantum Spaces'', Banach Center Publ. 40, Inst. Math. Polish Acad. Sci., Warszawa 1997, 111-137. [abs, src, ps]
  
• 18. Quantum supergroups of GL(n|m) type: differential forms, Koszul complexes and Berezinians, Duke Math. J. 90 (1997) n. 1, 1-62 (with A. Sudbery). [abs, src, ps]
  
• 19. Generalised Lie algebras of type A_n, J. Mathematical Phys. 39 (1998) n. 6, 3487-3504 (with A. Sudbery). [abs, src, ps]
  
• 21. Operations and isomorphisms in a triangulated Hopf category, Methods of Func. Analysis and Topology 5 (1999) n. 4, 37-53.
  
• 22. Integrals for braided Hopf algebras, J. Pure Appl. Algebra 148 (2000) n. 2, 113-164 (with Yu. Bespalov, T. Kerler, V. Turaev) [abs, src, ps]
  
• 25. On a functorial isomorphism in the derived category of l-adic sheaves, Matematychni Studii 14 (2000) n. 2, 115-120.
  
• 27. External tensor product of perverse sheaves, Ukrainian Math. J. 53 (2001), n. 3, 311-322. [abs, src, ps]
  
• 28. Operations in some graded Hopf categories, Preprint MPI 2001 - 44, unpublished.
  
• 29. Coassociativity-coherence relation for Hopf category n_+SL(2), Proc. 3rd Internat. Alg. Conf. in Ukraine, July 2-8 (Sumy), 2001, 67-70.
  
• 30. Tensor products of categories of equivariant perverse sheaves, Cahiers Topologie Geom. Differentielle Categ., XLIII-1 (2002), 49-79.
  
• 31. The triangulated Hopf category n_+SL(2), Appl. Categorical Struct. 10 (2002), n. 4, 331-381. [abs, src, ps]
  
• 32. A model of the 2-category of equivariant derived categories, Proc. of the First Ukrainian Math. Congress (Kyiv), August 2001, Inst. of mathematics NASU, 2002, 307-322.
  
• 33. Category of A_infinity-categories, Homology, Homotopy and Applications 5 (2003) n. 1, 1-48. [abs, src, ps]
  
• 36. Free A_infinity-categories, Theory and Applications of Categories 16 (2006) n. 9, 174-205 (with O. Manzyuk). [abs, src, ps]
  
• 38. A construction of quotient A_infinity-categories, Homology, Homotopy and Applications 8 (2006) n. 2, 157-203 (with S. Ovsienko). [abs, src, ps]
  
• 39. Unital A_infinity-categories, Problems of topology and related questions (V.V. Sharko, ed.), vol. 3, Proc. of Inst. of Mathematics NASU, Inst. of Mathematics, Nat. Acad. Sci. Ukraine, Kyiv, 2006, n. 3, 235-268 (with O. Manzyuk). [abs, src, ps]
  
• 40. Erratum to: ``Category of A_infinity-categories'' [Homology, Homotopy Appl. 5 (2003) no. 1, 1-48], Homology, Homotopy and Applications 9 (2007) n. 2, 163-164.
  
• 41. A_infinity-bimodules and Serre A_infinity-functors, Geometry and Dynamics of Groups and Spaces (M.M. Kapranov, S. Kolyada, Yu.I. Manin, P. Moree, and L. Potyagailo, eds.), Progress in Mathematics, vol. 265, Birkhauser Verlag, Basel, 2008, 565-645 (with O.~Manzyuk). [abs, src, ps]
  
• 42. Quotients of unital A_infinity-categories, Theory Appl. Categ. 20 (2008) n. 13, 405-496 (with O. Manzyuk). [abs, src, ps]
  
• 44. Homotopy unital A_infinity-algebras, J. Algebra 329 (2011) no. 1, 190-212, Special Issue Celebrating the 60th Birthday of Corrado De Concini. [abs, src, ps]
  
• 45. Bar and cobar constructions for curved algebras and coalgebras, Matematychni Studii 40 (2013) n. 2, 115-131. [abs, src, ps]
  
• 46. A_infinity-morphisms with several entries, Theory Appl. Categ. 30 (2015) n. 45, 1501-1551. [pdf]
  
• 47. Homotopy unital A_infinity-morphisms with several entries, Theory Appl. Categ. 30 (2015) n. 46, 1552-1623. [pdf]
  
• 48. Homotopy cooperads, Matematychni Studii 44 (2015) n. 2, 119-160. [pdf]
  
• 49. Curved homotopy coalgebras, Appl. Categ. Structures 25 (2017), no. 6, 991-1036. [abs, src, ps]
  
• 50. Moyal and Rankin-Cohen deformations of algebras, Proc. Int. Geom. Cent. 11 (2018), n. 2, 48-52. [pdf ]
  
• 51. A model structure on categories related to categories of complexes, Ukr. Math. J. 72 (2020) n. 2, 232-244. [pdf]
  
• 52. Filtered cocategories, Theory Appl. Categ. 35 (2020) n. 47, 1726-1770. [pdf]
  
• 53. Homotopy equivalence of normalized and unnormalized complexes, revisited, Algebra and Discrete Math., 32 (2021), no. 2, 253–266, (with A. Matsui), [pdf]
  
• 54. Dold-Kan correspondence, revisited, Appl. Categ. Structures 30 (2022), no. 3, 543-567. [pdf]