Noetherianity of some degree two twisted commutative algebras
By Rohit Nagpal, Steven V. Sam, Andrew Snowden. 2015
49 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/36652779cb226ec1a20cc1e51977ea60a90147ad
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In Algebra and Number Theory
- Jan Draisma
- Steven V. Sam
- Andrew Snowden
- Jenny Wilson
- Uwe Nagel
- Rohit Nagpal
- Thomas Church
- Tim Romer
In Geometry and Topology
- Jan Draisma
- Steven V. Sam
- Andrew Snowden
- Walter Gubler
- Eric Katz
- Andrew Putman
- Rohit Nagpal
- Jenny Wilson
Citations in the corpus
- Higher-order representation stability and ordered configuration spaces of manifolds (2016, unknown): “This is due to Nagpal–Sam–Snowden who address the case when n is odd [29, Theorem 1.1] and the case when n is even [30, .”
- Topological Noetherianity of polynomial functors (2017, background): “enerated Vec-modules over it? These questions were first raised, in the setting of twisted commutative algebras, in [Sno13]. They remain widely open, apartfrom progress in degree2 and characteristic 0 [NSS16]—but at least their topological counterparts are now settled. Acknowledgments. IthankArthurBi”
- STABILITY PATTERNS IN REPRESENTATION THEORY (2013, background): “m(V⊕n) are much more complicated, as they enter the realm of unbounded tca’s. We expect that Sym(Sym2(V)) and Sym( V2 (V)) might be tractable to analyze, however, and in recent joint work with Nagpal [NSS], the categories Rep(O) and Rep(Sp) served an essential role in establishing that these algebra”