Related papers: Incidence bicomodules, M\"obius inversion, and a R…

The space of invariants for a single matrix is generated by traces containing at most $N$ matrices per trace. We extend this analysis to multi-matrix models at finite $N$. Using the Molien-Weyl formula, we compute partition functions for…

Modular invariance is a fundamental symmetry in string compactifications, constraining both the structure of the effective theory and the dynamics of moduli and matter fields. It has also gained renewed importance in the context of…

The paper presents a detailed description of duality for braided algebras, coalgebras, bialgebras, Hopf algebras and their modules and comodules in the infinite setting. Assuming that the dual objects exist, it is shown how a given braiding…

It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…

The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.

We generalize the notion of `diagonal' from the class of CSL algebras to masa bimodules. We prove that a reflexive masa bimodule decomposes as a sum of two bimodules, the diagonal and a module generalizing the w*-closure of the Jacobson…

Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…

Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories.…

Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…

Let $C$ and $R$ be unital rings and $Z$ an injective cogenerator for right $C$-modules. For an $R,C$-bimodule $U$ let $U^*=Hom_C(U,Z)$, $S=End_R(U)$ and $Biend_R(U)=End_S(U)$, the biendomorphism ring of $U$. Under suitable requirements on…

Let $R$ be a ring, and consider a left $R$-module given with two (generally infinite) direct sum decompositions, $A\oplus(\bigoplus_{i\in I} C_i)=M=B\oplus(\bigoplus_{j\in J} D_j),$ such that the submodules $A$ and $B$ and the $D_j$ are…

We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-preserving automorphisms that fix a designated base world,…

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded…

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod $2$ cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by two,…

We present some tools for providing situations where the generalised Rota formula of arXiv:1801.07504 applies. As an example of this, we compute the M\"obius function of the incidence algebra of any directed restriction species, free…

Contramodules are module-like algebraic structures endowed with infinite summation (or, occasionally, integration) operations satisfying natural axioms. Introduced originally by Eilenberg and Moore in 1965 in the case of coalgebras over…