Let G be a finite group and let k be a field of characteristic p. It is known that a kG-module V carries a non-degenerate G-invariant bilinear form b if and only if V is self-dual. We show that whenever a Morita bimodule M which induces an equivalence between two blocks B(kG) and B(kH) of group algebras kG and kH is self-dual then the correspondence preserves self-duality. Even more, if the bil...

Let G be an affine algebraic group over an algebraically closed field k and let H be a closed subgroup of G. If V is a rational H-module (a comodule for the coordinate ring of H) there is a now well-known notion of an induced module VI G for G, defined as the space Morph/~(G, V) of all H-equivariant morphisms from G to a finite dimensional subspace of V, with obvious G-action. The question aris...

We construct a counterexample to Solel’s[25] conjecture that the range of any contractive, idempotent, MASA bimodule map on B(H) is necessarily a ternary subalgebra. Our construction reduces this problem to an analogous problem about the ranges of idempotent maps that are equivariant with respect to a group action. Such maps are important to understand Hamana’s theory of G-injective operator sp...

In this paper the Hochschild-cochain-complex of an A∞-algebra A with values in an A∞-bimodule M over A and maps between them is defined. Then, an∞-inner-product on A is defined to be an A∞-bimodule-map between A and its dual A∗. There is a graph-complex associated to A∞-algebras with ∞-inner-product.

Let R and S be arbitrary associative rings. Given a bimodule RWS , we denote by ∆? and Γ? the functors Hom?(−, W ) and Ext?(−, W ), where ? = R or S. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W , finitely generated or homomorphic image of a finite direct sum of copies of W , ΓM = 0 = Ext(M, W ). We are able to describe, on a larg...

Properties of (most general) non-commutative torsors or A-B torsors are analysed. Starting with pre-torsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is then concluded that every faithfully flat unital pre-torsor admits a (left and right) flat (bimodule) connection. It is shown that a class of faithfully flat pre-torsors induces equi...