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Draft:BGG correspondence

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Bernstein-Gelfand-Gelfand correspondence (BGG correspondence for short), established by Joseph Bernstein, Israel Gelfand, and Sergei Gelfand,[1] is an explicit triangulated equivalence that relates the bounded derived category of coherent sheaves on the projective space and the stable category of graded modules over the Exterior algebra . In the noncommutative setting, Martinez-Villa and Saorin R [2] generalized the BGG correspondence to finite-dimensional self-injective Koszul algebras with coherent Koszul duals . Roughly speaking, they proved that the stable category of finite-dimentional graded modules over a finite-dimensional self-injective Koszul algebra is triangulated equivalent to the bounded derived category of the category of coherent modules over its Koszul dual (when is coherent).

References

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  1. ^ Joseph Bernstein, Israel Gelfand, and Sergei Gelfand. Algebraic bundles over and problems of linear algebra. Funkts. Anal. Prilozh. 12 (1978); English translation in Functional Analysis and its Applications 12 (1978), 212-214
  2. ^ "Martínez-Villa, M. Saorín, Koszul equivalence and dualities", Pacific J. Math. 214 (2004) 359–378