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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
2
votes
Expressing properties of graded algebras in terms of the $\mathbb{G}_m$action
Expanding on Dylan Wilson's answer, condition (2) is indeed just a continuation of $\mathbb{G}_m$-action to an $\mathbb{A}^1$-action, since $\mathcal{O}(\mathbb{A}^1) \hookrightarrow \mathcal{O}(\math …
2
votes
Functors between categories of equivariant sheaves are equivariant sheaves on the product?
Let $G$ be a discrete group and $X$ a $G$-set. The equivariant category $X//G$ has elements of $X$ as objects, each triple $(g,x,g\cdot x)$ defines a morphism $x \to g\cdot x$, the composition corresp …