Related papers: Factorizable enriched categories and applications
We study some generalizations of the notion of regular crossed products K*G. For the case when K is an algebraically closed field, we give necessary and sufficient conditions for the twisted group ring K*G to be an n-weakly regular ring, a…
Are introduced six examples of non-braidable tensor categories which are extensions of the category Comod(H), for H a super-group algebra; and two examples of braided categories where the only possible braiding is the trivial braiding.
We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of…
The balanced tensor product M (x)_A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N. The balanced tensor product M [x]_C N of two module categories over a monoidal…
We analyze some relations between quasi-Hopf smash products and certain twisted tensor products of quasialgebras. Along the way we obtain also some results of independent interest, such as a duality theorem for finite dimensional quasi-Hopf…
In the previous paper arxiv:math/0610552 semisimple tensor categories were constructed out of certain regular Mal'cev categories. In this paper, we calculate the tensor product multiplicities and the categorical dimensions of the simple…
We introduce the concept of pseudotwistor (with particular cases called twistor and braided twistor) for an algebra $(A, \mu, u)$ in a monoidal category, as a morphism $T:A\otimes A\to A\otimes A$ satisfying a list of axioms ensuring that…
We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the…
We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.
A classical tensor product $A \,\otimes\, B$ of complete lattices $A$ and $B$, consisting of all down-sets in $A \times B$ that are join-closed in either coordinate, is isomorphic to the complete lattice $Gal(A,B)$ of Galois maps from $A$…
We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show…
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
In this work we define a class of injective-type norm on tensor products through the environment of sequence classes. Examples and results on this norm will be presented and the duality is studied in this context. As a byproduct, we present…
We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to…
We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms…
Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford…
In this paper we study twisted algebras of multiplier Hopf ($^*$-)algebras which generalize all kinds of smash products such as generalized smash products, twisted smash products, diagonal crossed products, L-R-smash products, two-sided…
We study twisted bialgebras and double twisted bialgebras, that is to say bialgebras in the category of linear species, or in the category of species in the category of coalgebras. We define the notion of cofree twisted coalgebra and…
Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…
Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…