G-algebras, Twistings, and Equivalences of Graded Categories

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Abstract

Given Z-graded rings A and B, we ask when the graded module categories gr-A and gr-B are equivalent. Using Z-algebras, we relate the Morita-type results of Ahn-Marki and del Rio to the twisting systems introduced by Zhang, and prove, for example: Theorem If A and B are Z-graded rings, then: (1) A is isomorphic to a Zhang twist of B if and only if the Z-algebras A = circle plus(i, j is an element of Z) A(j-i) and B = circle plus(i, j is an element of Z) Bj-i are isomorphic. (2) If A and B are connected graded with A1 not equal 0, then gr-A similar or equal to gr-B if and only if A and B are isomorphic. This simplifies and extends Zhang's results.

Original languageEnglish
Pages (from-to)377-390
Number of pages14
JournalAlgebras and representation theory
Volume14
Issue number2
DOIs
Publication statusPublished - Apr 2011

Keywords

  • Graded module category
  • Category equivalence
  • Graded Morita theory
  • Twisting system
  • Z-algebra
  • Graded domain
  • RINGS

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