Sp-equivariant modules over polynomial rings in infinitely many variables
| Autor: | Sam, Steven V, Snowden, Andrew |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. 375 (2022), 1671-1701 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/8496 |
| Popis: | We study the category of Sp-equivariant modules over the infinite variable polynomial ring, where Sp denotes the infinite symplectic group. We establish a number of results about this category: for instance, we show that every finitely generated module M fits into an exact triangle $T \to M \to F \to$ where T is a finite length complex of torsion modules and F is a finite length complex of "free" modules; we determine the Grothendieck group; and we (partially) determine the structure of injective modules. We apply these results to show that the twisted commutative algebras ${\rm Sym}({\bf C}^{\infty} \oplus \bigwedge^2{\bf C}^{\infty})$ and ${\rm Sym}({\bf C}^{\infty} \oplus {\rm Sym}^2{\bf C}^{\infty})$ are noetherian, which are the strongest results to date of this kind. We also show that the free 2-step nilpotent twisted Lie algebra and Lie superalgebra are noetherian. Comment: 29 pages |
| Databáze: | arXiv |
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