Related papers: Torsorial actions on G-crossed braided tensor cate…

A modular category $\mathcal{C}$ gives rise to a differential graded modular functor, i.e. a system of projective mapping class group representations on chain complexes. This differential graded modular functor assigns to the torus the…

We prove that if a finite group $G$ acts outerly on a McDuff $\rm II_1$ factor $M$, then $\mathsf{Rep}(G/KL)$ is a braided monoidal full subcategory of the categorical Connes' $\tilde{\chi}(M\rtimes G)$ defined in arXiv:2111.06378, where…

We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…

In our recent papers [Sh1,2], we introduced a {\it twisted tensor product} of dg categories, and provided, in terms of it, {\it a contractible 2-operad $\mathcal{O}$}, acting on the category of small dg categories, in which the "natural…

We introduce the notions of Koszul $N$-complex, $\check{\mathrm{C}}$ech $N$-complex and telescope $N$-complex, explicit derived torsion and derived completion functors in the derived category $\mathbf{D}_N(R)$ of $N$-complexes using the…

We study the categorical type A action on the Deligne category $\mathcal{D}_t=\underline{Rep}(GL_t)$ (here $t \in \mathbb{C}$) and its "abelian envelope" $\mathcal{V}_t$ constructed in arXiv:1511.07699. For $t \in \mathbb{Z}$, this action…

We introduce a notion of I-factorial quantum torsor, which consists of an integrable ergodic action of a locally compact quantum group on a type I-factor such that also the crossed product is a type I-factor. We show that any such…

We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…

Given an algebra with group $G$-action, we construct brace structures for its $G$-twisted Hochschild cochains. An an application, we construct $G$-Frobenius algebras for orbifold Landau-Ginzburg B-models and present explicit orbifold cup…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Let $G$ be the group of all order-preserving self-maps of the real line. In previous work, the first two authors constructed a pre-Tannakian category $\underline{\mathrm{Rep}}(G)$ associated to $G$. The present paper is a detailed study of…

Given a suitable stable monoidal model category $\mathscr{C}$ and a specialization closed subset $V$ of its Balmer spectrum one can produce a Tate square for decomposing objects into the part supported over $V$ and the part supported over…

Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. We…

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

In a strengthening of the G-Signature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant K-homology of the signature operator on…

This is the first of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). In the present text, as a starting point, we define the…

Let R be a discrete valuation ring of unequal characteristic with fraction field K which contains a primitive p^2-th root of unity. Let X be a faithfully flat R-scheme and G be a finite abstract group. Let us consider a G-torsor Y_K\to X_K…

We show that every action operad gives rise to a notion of monoidal category via the categorical version of the Borel construction, embedding action operads into the category of 2-monads on $\mathbf{Cat}$. We characterize those 2-monads in…

Following Nori's original idea we here provide certain motivic categories with a canonical tensor structure. These motivic categories are associated to a cohomological functor on a suitable base category and the tensor structure is induced…

Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…