Positions

Publications

Academic Article

Year Title
2018 On the Brauer-Picard groups of fusion categoriesMathematische Zeitschrift.  288:689-712. 2018
2015 On the Brauer-Picard group of a finite symmetric tensor categoryJournal of Algebra.  440:187-218. 2015
2014 Categorical Lagrangian Grassmannians and Brauer-Picard groups of pointed fusion categoriesJournal of Algebra.  411:191-214. 2014
2013 The Witt group of non-degenerate braided fusion categoriesJournal fur die Reine und Angewandte Mathematik.  677:135-177. 2013
2013 On the structure of the Witt group of braided fusion categoriesSelecta Mathematica, New Series.  19:237-269. 2013
2013 Morita equivalence methods in classification of fusion categoriesHOPF ALGEBRAS AND TENSOR CATEGORIES.  585:289-325. 2013
2013 The Picard crossed module of a braided tensor categoryAlgebra and Number Theory.  7:1365-1403. 2013
2011 Weakly group-theoretical and solvable fusion categoriesAdvances in Mathematics.  226:176-205. 2011
2010 On braided fusion categories ISelecta Mathematica, New Series.  16:1-119. 2010
2009 Centers of graded fusion categoriesAlgebra and Number Theory.  3:959-990. 2009
2009 Fusion Subcategories of Representation Categories of Twisted Quantum Doubles of Finite GroupsInternational Mathematics Research Notices International Mathematics Research Papers.  22:4183-4219. 2009
2008 Non-group-theoretical semisimple Hopf algebras from group actions on fusion categoriesSelecta Mathematica, New Series.  14:145-161. 2008
2008 Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groupsCommunications in Mathematical Physics.  279:845-872. 2008
2008 Nilpotent fusion categoriesAdvances in Mathematics.  217:1053-1071. 2008
2005 On fusion categoriesAnnals of Mathematics.  162:581-642. 2005
2004 Semisimple weak Hopf algebrasJournal of Algebra.  275:639-667. 2004
2004 An analogue of Radford's S-4 formula for finite tensor categoriesInternational Mathematics Research Notices International Mathematics Research Papers.  2915-2933. 2004
2003 Invariants of knots and 3-manifolds from quantum groupoidsTopology and its Applications General Topology and its Applications.  127:91-123. 2003
2002 On twisting of finite-dimensional Hopf algebrasJournal of Algebra.  256:484-501. 2002
2002 On the structure of weak Hopf algebrasAdvances in Mathematics.  170:257-286. 2002
2002 Outer actions of centralizer Hopf algebras on separable extensionsCommunications in Algebra.  30:383-410. 2002
2001 Hopf algebra actions on strongly separable extensions of depth twoAdvances in Mathematics.  163:258-286. 2001
2001 Frobenius extensions and weak Hopf algebrasJournal of Algebra.  244:312-342. 2001
2001 Dynamical quantum groups at roots of 1Duke Mathematical Journal.  108:135-168. 2001
2001 Vertex-IRF transformations and quantization of dynamical r-matricesMathematical Research Letters.  8:331-345. 2001
2001 Duality for actions of weak Kac algebras and crossed product inclusions of II1 factorsJournal of Operator Theory.  46:635-655. 2001
2001 Dynamical twists in group algebrasInternational Mathematics Research Notices International Mathematics Research Papers.  679-701. 2001
2000 A Galois correspondence for II1 factors and quantum groupoidsJournal of Functional Analysis.  178:113-142. 2000
2000 A characterization of depth 2 subfactors of II1 factorsJournal of Functional Analysis.  171:278-307. 2000
2000 Algebraic versions of a finite-dimensional quantum groupoidLecture Notes in Pure and Appl. Math, 209 (2000), 189-221.  209:189-220. 2000
1998 K-0-rings and twisting of finite dimensional semisimple Hopf algebrasCommunications in Algebra.  26:321-342. 1998
1998 K-0-rings and twisting of finite dimensional semisimple Hopf algebras (vol 26, Pg 321, 1998)Communications in Algebra.  26:2019-2019. 1998
1998 K-0-rings and twisting of finite dimensional semisimple Hopf algebras (vol 26, pg 321, 1998)Communications in Algebra.  26:1347-1347. 1998
A Duality Theorem for Quantum GroupoidsContemporary Mathematics, volume 267, pp. 237-243.
Autoequivalences of tensor categories attached to quantum groups at roots of $1$
Finite Quantum Groupoids and Their Applications
Fusion categories and homotopy theory
Group-theoretical properties of nilpotent modular categories
Pointed braided tensor categories
Vertex-IRF transformations and quantization of dynamical r-matricesMath. Res. Letters.  8:3.

Teaching Activities

  • Algebra II Taught course 2019
  • Combinatorics Taught course 2019
  • Algebra I Taught course 2018
  • Foundations of Number Theory Taught course 2018
  • Ind Stdy/Intro to Repre Theory Taught course 2018
  • Algebraic Structures Taught course 2018
  • Algebra II Taught course 2018
  • Combinatorics Taught course 2018
  • Abstract Algebra Taught course 2017
  • Algebra I Taught course 2017
  • Algebra II Taught course 2017
  • Combinatorics Taught course 2017
  • Algebra I Taught course 2016
  • Foundations of Number Theory Taught course 2016
  • Theory of Numbers for Teachers Taught course 2016
  • Algebra II Taught course 2016
  • Combinatorics Taught course 2016
  • Algebra I Taught course 2015
  • Mathematical Proof Taught course 2015
  • Algebra II Taught course 2015
  • Multidimensional Calculus Taught course 2015
  • Algebraic Structures Taught course 2014
  • Algebra II Taught course 2014
  • Topics in Algebra I Taught course 2014
  • Education And Training

    Full Name

  • Dmitri Nikshych