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We develop methods of computation of the Brauer-Picard groups of fusion categories and apply them to compute such groups for several classes of fusion categories of prime power dimension: representation categories of elementary abelian groups with twisted associativity constraint, extra special p-groups, and the Kac-Paljutkin Hopf algebra.
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S. Gelaki, D. Nikshych, Nilpotent fusion categories. Advances in Mathematics
2008
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D. Naidu, D. Nikshych, Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups
2008
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S. Gelaki, D. Naidu, and D. Nikshych, Centers of graded fusion categories
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2012
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A. Davydov, M. Müger, D. Nikshych, and V. Ostrik, The Witt group of non-degenerate braided fusion categories
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C. Galindo, J. Plavnik, Tensor functor between Morita duals of fusion categories
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G. Mason, S.-H. Ng, Cleft extensions and quotients of twisted quantum doubles
2014
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B. Riepel, Brauer-Picard groups of pointed fusion categories
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2009
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D. Naidu, D. Nikshych, and S. Witherspoon, Fusion subcategories of representation categories of twisted quantum doubles of finite groups
2009
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R.A. Wilson, The finite simple groups
2009
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V. Drinfeld, S. Gelaki, D. Nikshych, and V. Ostrik, On braided fusion categories I
2010
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P. Etingof, D. Nikshych, and V. Ostrik, Fusion categories and homotopy theory
2010
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P. Etingof, D. Nikshych, and V. Ostrik, Weakly group-theoretical and solvable fusion categories
2011
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2014
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C. Bontea, D. Nikshych, On the Brauer-Picard group of a finite symmetric tensor category
2015
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P. Etingof, S. Gelaki, D. Nikshych, V. Ostrik, Tensor categories
2015
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2015
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B. Uribe, On the classification of pointed fusion categories up to weak Morita equivalence
2015
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