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Using the Steinberg algebra model to determine the center of any Leavitt path algebra
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Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization of compact open invariant subsets of the unit space of the graph groupoid in terms of the underlying graph: an open invariant subset is compact if and only if its associated hereditary and saturated set of vertices satisfies Condition (F). We also give a basis of the center. Its cardinality depends on the number of minimal compact open invariant subsets of the unit space.
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Monoidal structures arising from $B_\infty$-algebras with applications to Hopf algebras
A B-infinity structure on an algebra gives a monoidal tensor product on the derived category of right modules, and for Hopf algebras this produces an algebraic proof of the Benson-Krause monoidal equivalence.
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