相关论文: Morita base change in quantum groupoids

We construct a 2-category version of tom Dieck's equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; hence an orbifold invariant for representable orbifolds.

We study Morita equivalence in the context of quantales with identity, in the wake of Katsov and Nam's analogous work on semirings. Among a number of other results, we prove a characterization of Morita equivalence and an…

We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…

We defined a notion of quantum 2-torus $T_\theta$ in "Masanori Itai and Boris Zilber, Notes on a model theory of quantum 2-torus $T_q^2$ for generic $q$, arXiv:1503.06045v1 [mathLO]" and studied its model theoretic property. In this note we…

Let $S$ be a Rees semigroup, and let $\ell^1(S)$ be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of $\ell^1(S)$ is isomorphic to those of the underlying discrete group…

In this note we recall some recent progress in understanding the representation theory of *-algebras over rings C = R(i) where R is ordered and i^2 = -1. The representation spaces are modules over auxiliary *-algebras with inner products…

We extend Schur-Weyl duality to an arbitrary level $l \geq 1$, the case $l=1$ recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke…

We relate group quotients of dg-categories and linear stable $\infty$-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also…

The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…

A surjective Morita context connecting semigroups $S$ and $T$ yields a Morita semigroup and a strict local isomorphism from it onto $S$ along which idempotents lift. We describe strong Morita equivalence of firm semigroups in terms of…

We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including the ordinary Hamiltonian $G$-spaces, Lu's…

We introduce Morita equivalence to the study of Kleene algebras and modules. Classical characterizations of Morita-equivalent semirings such as having equivalent categories of modules and one semiring being a full matrix algebra over the…

Non-perturbative partition functions of quantum theories constitute a class of $\tau-$functions, which are distinguished satisfying Hirota's bilinear identities(BI). To make this statement general, there must be a proper definition of…

We propose an analogue of the bounded derived category for an augmented ring spectrum, defined in terms of a notion of Noether normalization. In many cases we show this category is independent of the chosen normalization. Based on this, we…

A homotopy analogue of the notion of a triangular Lie bialgebra is proposed with a goal of extending the basic notions of theory of quantum groups to the context of homotopy algebras and, in particular, introducing a homotopical…

The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…

Let $G$ and $H$ be Hausdorff ample groupoids and let $R$ be a commutative unital ring. We show that if $G$ and $H$ are equivalent in the sense of Muhly-Renault-Williams, then the associated Steinberg algebras of locally constant $R$-valued…

We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…

We investigate the equivariant and Hopf-cyclic cohomology of module algebras over Hopf algebroids and derive their Morita invariance. For this, we use the tools developed by McCarthy for $k$-linear categories and subsequently by Kaygun and…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…