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Creators/Authors contains: "Laudone, Robert"

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  1. ; (, Transactions of the American Mathematical Society)
    Let A A be a commutative algebra equipped with an action of a group G G . The so-called G G -primes of A A are the equivariant analogs of prime ideals, and of central importance in equivariant commutative algebra. When G G is an infinite dimensional group, these ideals can be very subtle: for instance, distinct G G -primes can have the same radical. In previous work, the second author showed that if G = G L ∞ G=\mathbf {GL}_{\infty } and A A is a polynomial representation, then these pathologies disappear when G G is replaced with the supergroup G L ∞ | ∞ \mathbf {GL}_{\infty |\infty } and A A with a corresponding algebra; this leads to a geometric description of G G -primes of A A . In the present paper, we construct an abstract framework around this result, and apply the framework to prove analogous results for other (super)groups. We give some applications to the isomeric determinantal ideals (commonly known as “queer determinantal ideals”). 
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  2. (, Proceedings of the American Mathematical Society)
    We resolve an open question posed by Nagpal, Sam and Snowden [Selecta. Math. (N.S.) 22 (2016), pp. 913–937] in 2015 concerning a Gröbner theoretic approach to the noetherianity of the twisted commutative algebra S y m ( S y m 2 ( C ∞ ) ) Sym(Sym^2(\mathbf {C}^\infty )) . We provide a negative answer to their question by producing an explicit antichain. In doing so, we establish a connection to well-studied posets of graphs under the subgraph and induced subgraph relation. We then analyze this connection to suggest future paths of investigation. 
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  3. ; ; ; ; ; ; (, Journal of Software for Algebra and Geometry)
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