Related papers: Tensor triangular geometry of non-commutative moti…
We introduce the notion of hyperbolic orientation of a motivic ring spectrum, which generalises the various existing notions of orientation (by the groups GL, SLc, SL, Sp). We show that hyperbolic orientations of eta-periodic ring spectra…
We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated…
In this article we further the study of the relationship between pure motives and noncommutative motives. Making use of Hochschild homology, we introduce the category NNum(k)_F of noncommutative numerical motives (over a base ring k and…
We start by developing a theory of noncommutative (=NC) mixed motives with coefficients in any commutative ring. In particular, we construct a symmetric monoidal triangulated category of NC mixed motives, over a base field k, and a full…
We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all…
For polynomial representations of $GL_n$ of a fixed degree, H. Krause defined a new internal tensor product using the language of strict polynomial functors. We show that over an arbitrary commutative base ring $k$, the Schur functor…
We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphisms of motivic dga's can reasonably be thought of as a…
We introduce the notion of composition series of triangulated categories, which generalizes full exceptional sequences. The lengths of composition series yield invariants for triangulated categories. We study composition series of derived…
In this paper, perfect k-orthogonal colourings of tensor graphs are studied. First, the problem of determining if a given graph has a perfect 2-orthogonal colouring is reformulated as a tensor subgraph problem. Then, it is shown that if two…
Let $G$ be a reductive algebraic group over a perfect field $k$ and $\cG$ a $G$-bundle over a scheme $X/k$. The main aim of this article is to study the motive associated with $\cG$, inside the Veovodsky Motivic categories. We consider the…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
Let $k$ be a field of characteristic $0$ endowed with a complex embedding $\sigma: k \hookrightarrow \mathbb{C}$. In this paper we complete the construction of the six functor formalism on perverse Nori motives over quasi-projective…
Category theoretic aspects of non-rational conformal field theories are discussed. We consider the case that the category C of chiral sectors is a finite tensor category, i.e. a rigid monoidal category whose class of objects has certain…
Inspired by the study of vertex operator algebra extensions, we answer the question of when the category of local modules over a commutative exact algebra in a braided finite tensor category is a (non-semisimple) modular tensor category.…
We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars ACG in the sense…
Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics,…
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…
As a higher genus version of universal mixed elliptic motives by Hain and Matsumoto, we consider mixed Teichm\"uller motives as certain motivic local systems on the moduli space of pointed curves. We show that the category of mixed…
In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…
In a number of recent works [6, 7] the authors have introduced and studied a functor $\mathcal{F}_k$ which associates to each loose graph $\Gamma$ -which is similar to a graph, but where edges with $0$ or $1$ vertex are allowed - a…