Sesión Álgebra, Álgebra Conmutativa, Teoría de GruposGlobalization of Hochschild homology and smooth algebras
Eduardo Marcos
IME-USP, Brasil - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
For a unital partial action \(\alpha\) of a group \(G\) on an associative unital algebra \(A\) with a unital globalization \((\{\Theta_g\}_{g\in G},\mathcal{W})\), we prove a natural isomorphism \[\Lambda\big(HH_{\bullet}(A,M)\big)\cong HH_{\bullet}\big(\mathcal{W},\mathfrak{A}(M)\big)\] for any covariant \(A\)-bimodule \(M\). In particular if \(M=A\), we obtain an isomorphism between their respective Hochschild homologies: \(\Lambda\big(H_{\bullet}(A)\big)\cong H_{\bullet}\big(\mathcal{W}\big)\).
Here \(\mathfrak{A}\) is an exact functor relating the categories of covariant bimodules, while \(\Lambda\) is the exact globalization functor for partial representations of \(G\). As an application, we show that under standard finiteness conditions, a commutative algebra \(A\) is smooth if and only if its globalization \(\mathcal{W}\) is smooth.
Trabajo en conjunto con: Mikhailo Dokuchaev y Emmanuel Jerez.