Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either ‖Φ‖ > η6 or ‖Φ‖ = ηk for some k ∈ {0, 1, 2, 3, 4, 5, 6}. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm ηk for 0 ≤ k ≤ 6. We also show that the Schur idempote...

We describe obstructions to a direct limit preserving right exact functor between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, all obstructions vanish and we recover the Eilenberg-Watts Theorem. We use our description of these obstructions to prove that if a direct limit preserving right exact functor F from a s...

A triangular matrix algebra over a field k is defined by a triplet (R, S, M) where R and S are k-algebras and RMS is an SR-bimodule. We show that if R, S and M are finite dimensional and the global dimensions of R and S are finite, then the triangular matrix algebra corresponding to (R, S, M) is derived equivalent to the one corresponding to (S, R, DM), where DM = Homk(M, k) is the dual of M , ...

Abstract For ℳ and $$ \mathcal{N} N finite module categories over a tensor category \mathcal{C} C , the \mathrm{\mathcal{R}}{ex}_{\mathcal{C}} ℛ ex (ℳ, ) of right exact functors is Drinfeld center \mathcal{Z} Z ( ). We ...

Beliakova-Putyra-Wehrli studied various kinds of traces, in relation to annular Khovanov homology. In particular, a graded algebra and bimodule over it, they associate quantum Hochschild homology the with coefficients bimodule, use this obtain deformation link. A spectral refinement resulting invariant was recently given by Akhmechet-Krushkal-Willis. short note we observe that is composition tw...

We prove the extended Hilbert’s Nullstellensatz in the context of Hu-Liu polynomial trirings. Which kinds of noncommutative rings are suitable for extending algebra geometry? Different attempts have been made to answer this question, but a satisfactory answer is still in hiding. My attempt at answering this question comes from the trivial extension of a ring by a bimodule over the ring. The tri...

It was recently shown (by the second author and D\'{i}az Garc\'{i}a, Krutov, Somberg, Strung) that every relative line module over an irreducible quantum flag manifold $\mathcal{O}_q(G/L_S)$ admits a unique $\mathcal{O}_q(G)$-covariant connection with respect to Heckenberger-Kolb differential calculus $\Omega^1_q(G/L_S)$. In this paper we show these connections are bimodule invertible associate...

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C∗-correspondences and Cuntz– Pimsner algebras. We show that the C∗-algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura’s topological-graph bimodule, and that the C∗-algebra generated by...