Noetherianity of some degree two twisted commutative algebras

• Rohit Nagpal ^[2] ; Steven V Sam ^[3] ; Andrew Snowden ^[1]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  2. [2] University of Wisconsin
  3. [3] University of California,

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 913-937
• Idioma: inglés
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• Resumen

  • The resolutions of determinantal ideals exhibit a remarkable stability property: for fixed rank but growing dimension, the terms of the resolution stabilize (in an appropriate sense). One may wonder if other sequences of ideals or modules over coordinate rings of matrices exhibit similar behavior. We show that this is indeed the case. In fact, our main theorem is more fundamental in nature: It states that certain large algebraic structures (which are examples of twisted commutative algebras) are noetherian. These are important new examples of large noetherian algebraic structures, and ones that are in some ways quite different from previous examples.