Mini-course on twisted commutative algebras
نویسنده
چکیده
The first is representation stability: a generalization of homological stability in the presence of group actions which was introduced by Church and Farb. For symmetric group actions, this is formalized in the notion of FI-modules, introduced by Church, Ellenberg, and Farb. FI-modules turn out to be modules over a twisted commutative algebra (the free tca generated by 1 element of degree 1). The study of this tca reveals deeper algebraic properties of FI-modules (we will spend a lot of time on this tca). The study of general tca’s is relevant for generalized versions of FI-modules.
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