Noetherianity of some degree two twisted skew-commutative algebras

• Rohit Nagpal ^[1] ; Steven V. Sam ^[3] ; Andrew Snowden ^[2]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
  2. [2] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  3. [3] University of Wisconsin, USA

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 1, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0461-3
• Enlaces
  • Texto completo (pdf)
• Resumen

  • A major open problem in the theory of twisted commutative algebras (tca’s) is proving noetherianity of finitely generated tca’s. For bounded tca’s this is easy; in the unbounded case, noetherianity is only known for Sym(Sym2(C∞)) and Sym(⋀2(C∞)) . In this paper, we establish noetherianity for the skew-commutative versions of these two algebras, namely ⋀(Sym2(C∞)) and ⋀(⋀2(C∞)) . The result depends on work of Serganova on the representation theory of the infinite periplectic Lie superalgebra, and has found application in the work of Miller–Wilson on “secondary representation stability” in the cohomology of configuration spaces.